Trigonometry Questions with solution for Competitive Exams. Previous year Exam Question with official answer and detail explanation with short tricks. The Questions are as per SSC CGL and CHSL Exam Syllabus and Pattern. The below 1-18 questions are from the all shifts of SSC CHSL Exam.
Trigonometry Questions with Solution
Q.1: If (sin A – cos A) = 0 , then what is the value of cot A ?
(A)
(B) 0
(C) 1
(D)
Show Answer
(sin A – cos A) = 0
sin A = cos A
![Rendered by QuickLaTeX.com \frac{cos A}{sin A} = 1](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e0886cfdae1379ab6bd4038386dfda27_l3.png)
cot A = 1
Q.2: If and
is an acute angle, then the value of
will be:
(A)
(B)
(C)
(D)
Show Answer
![Rendered by QuickLaTeX.com \frac 98](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-a82c0776925677bc3440651c8921878f_l3.png)
![Rendered by QuickLaTeX.com cosec\theta=\frac{41}{9}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-bfc9fa330d5f4bda4dd821e233f81e1f_l3.png)
![Rendered by QuickLaTeX.com sin\theta=\frac{9}{41}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-778d354938108820118fc424348fc5bf_l3.png)
पाइथागोरस प्रमेय से
BC2 = 412 – 92
![Rendered by QuickLaTeX.com BC =\sqrt{1600} = 40](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e77bad6baca1eb48551a549618dcd6a1_l3.png)
ATQ
![Rendered by QuickLaTeX.com 5 tan\theta = 5\times \frac{9}{40}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-bf070b2f6acfe93b7f189de59b69f3f7_l3.png)
![Rendered by QuickLaTeX.com =\frac98](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-8cf9965f1b4d2962294d67a1af9dfe01_l3.png)
Q.3: Solve the following equation and find the value of .
(A) 60o
(B) 30o
(C) 15o
(D) 45o
Show Answer
![Rendered by QuickLaTeX.com 3 cot\theta + tan \theta -2\sqrt3 = 0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-d4c750ec223d7dba76a097fe512eaebc_l3.png)
Put
![Rendered by QuickLaTeX.com \theta = 60](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-7858ab2df129089e32b45ee89313415e_l3.png)
3 x cot60 + tan60 -2
![Rendered by QuickLaTeX.com \sqrt{3}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-6d8fcb410497e3f0d2c53c30482e0f47_l3.png)
![Rendered by QuickLaTeX.com 3\times\frac{1}{\sqrt3} +\sqrt3 - 2\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-33a51447e255694be44a39541b96da71_l3.png)
![Rendered by QuickLaTeX.com \frac{3}{\sqrt3} +\sqrt3 - 2\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-634e1c630de9e0ac45823714d963c89f_l3.png)
![Rendered by QuickLaTeX.com \frac{6}{\sqrt3} -2\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c05c0ab904716d7d0f31ef925218b058_l3.png)
![Rendered by QuickLaTeX.com \frac {6-6}{\sqrt3} = \frac{0}{\sqrt3} = 0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-700978e9592ec8ab84771ebdc55e31f8_l3.png)
so
![Rendered by QuickLaTeX.com \theta = 60](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-7858ab2df129089e32b45ee89313415e_l3.png)
Q.4: In ,
, AB = 20cm and BC = 29cm. What is the value of (sinB -cotC) ?
(A)
(B)
(C)
(D)
Show Answer
![Rendered by QuickLaTeX.com -\frac{189}{580}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3d3151c5ecefdee534c1de82d8ac12fe_l3.png)
![Trigonometry Questions for Competitive Exams](https://sscstudy.com/wp-content/uploads/2021/12/image-20.png)
Q.5: If tanx = cot(48o + 2x), and 0o <x <90o , then what is the value of x ?
(A) 14o
(B 12o
(C) 21o
(D) 16o
Show Answer
tan x = cot (48 + 2x)
tanx = tan (90 – (48 + 2x)
x = 90 -(48 + 2x)
x = 90 – 48 – 2x
3x = 42
x = 14
Q.6: If , then the value of
will be:
(A) 45o
(B) 30o
(C) 60o
(D) 75o
Show Answer
![Rendered by QuickLaTeX.com 7 sin^2\theta + 3cos^2\theta = 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-111677cc8d6be00f06e70286cc6e44b9_l3.png)
![Rendered by QuickLaTeX.com 4 sin^2\theta + 3sin^2\theta +3cos^2\theta= 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-35fc8d1ebdd6122208273e4950ecdfea_l3.png)
![Rendered by QuickLaTeX.com 4 sin^2\theta + 3(sin^2 \theta + cos^2\theta)= 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-79b2667616399af2d107e9e80b78a7bd_l3.png)
![Rendered by QuickLaTeX.com 4sin^2\theta + 3\times1 = 4](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-277c03146144629e9ebc4bbc288d9ae8_l3.png)
![Rendered by QuickLaTeX.com 4sin^2\theta = 4 - 3 = 1](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-054abfce85006c83611eab9c2933bccf_l3.png)
![Rendered by QuickLaTeX.com sin^2\theta =\frac 14](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-38685b4c901bf7ec8cb2239f84e7a4d7_l3.png)
![Rendered by QuickLaTeX.com sin\theta =\frac 12](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0018f4c434d5242a0c00daf095fe37ed_l3.png)
![Rendered by QuickLaTeX.com \theta = 30^o](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-716d28a12970be166daf14c8bd27ac27_l3.png)
Q.7: Find the value of , If sec2
, where
is an acute angle.
(A) 30o
(B) 15o
(C) 60o
(D) 45o
Show Answer
![Rendered by QuickLaTeX.com sec^2\theta +(1 -\sqrt3) tan\theta -(1 +\sqrt3) =0](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-896bd8aab8ee80f76de723a299046eb4_l3.png)
put
![Rendered by QuickLaTeX.com \theta = 60^o](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0c3c29d0577ff15552bc62d37e83ef71_l3.png)
![Rendered by QuickLaTeX.com sec^2(60) + (1 -\sqrt3) tan 60 - (1 +\sqrt3)](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0ef9f93cd57e610083d20d4024a8de41_l3.png)
![Rendered by QuickLaTeX.com 4 +(1 - \sqrt3) \sqrt3 - (1 + \sqrt3)](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-761907b5c1488cea3f129b68638d88cb_l3.png)
![Rendered by QuickLaTeX.com 4 +\sqrt3 - 3 - 1 -\sqrt3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-49738a6ea836b17ce97b71a6f69b2247_l3.png)
4 – 4 = 0
So
![Rendered by QuickLaTeX.com \theta = 60](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-7858ab2df129089e32b45ee89313415e_l3.png)
Q.8: If and
is an acute angle, then the value of
is:
(A) 15
(B) 12
(C) 1
(D) 9
Show Answer
![Trigonometry Questions for Competitive Exams](https://sscstudy.com/wp-content/uploads/2021/12/image-19.png)
Q.9: In a triangle ABC , right-angled at C, if sec A , then find the value of
.
(A)
(B) 5
(C)
(D)
[toggle] Ans : (D)
![Trigonometry Questions for Competitive Exams](https://sscstudy.com/wp-content/uploads/2021/12/image-21.png)
Q.10: If , then what is the value of
?
(A) 322
(B) 382
(C) 367
(D) 350
Show Answer
![Rendered by QuickLaTeX.com sin\theta + cosec \theta = 7](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-e7f9130fc88fcb591e8f4f1bf252ac56_l3.png)
![Rendered by QuickLaTeX.com (sin\theta + cosec \theta)^3 = 7^3](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-2df1e8950048408962ab2106671bd7db_l3.png)
![Rendered by QuickLaTeX.com sin^3\theta + cosec^3 \theta +3sin\theta cosec\theta\times7 = 343](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-a12ddf8381f7015739b5b52ce8d6bccc_l3.png)
![Rendered by QuickLaTeX.com sin^3\theta + cosec^3 \theta +3\times7 = 343](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-361af8b93c3122cd4cacde4210c4a370_l3.png)
![Rendered by QuickLaTeX.com Sin\theta\times Cosec\theta = 1](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-22d39de4d9626fb07ce45f2c013a386d_l3.png)
![Rendered by QuickLaTeX.com sin^3\theta + cosec^3\theta = 343 - 21 = 322](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-9d3d1550ed803c9ba19361bf5352071c_l3.png)
Trigonometry Questions for Competitive Exams
Q.11: If 3 cot A = 4 tan A , and A is an acute angle, then what will be the value of Sec A ?
(A)
(B)
(C)
(D)
Show Answer
![Rendered by QuickLaTeX.com \frac{\sqrt7}{2}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-6514acf43d193df9aca4ba37ad7e71df_l3.png)
![](https://sscstudy.com/wp-content/uploads/2021/12/image-23.png)
Q.12: What is the value of ?
(A) -1
(B) 0
(C) -2
(D) 1
Show Answer
![Rendered by QuickLaTeX.com \frac{cos^220^o + cos^270^o}{sin^290^o} -tan^245^o](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-04b8fd8c1359db3be2fa77ba22a5345f_l3.png)
![Rendered by QuickLaTeX.com \frac{1}{1} -1](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-c52f138593ac6e3b614ab491715824db_l3.png)
= 0
Q.13: If , then the value of
is:
(A) 5
(B)
(C) 3
(D) 4
Show Answer
![](https://sscstudy.com/wp-content/uploads/2021/12/image-30.png)
Q.14: In a right-angled triangle ABC right angled at C, Sin A = Sin B. What is the value of Cos A ?
(A) 1
(B)
(C)
(D)
Show Answer
![Rendered by QuickLaTeX.com \frac{1}{\sqrt2}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0a80153039534180e29c7a3a16700a3c_l3.png)
Sin A = Sin B
A = B = 45 Satisfy
Cos A = Cos 45
=
![Rendered by QuickLaTeX.com \frac{1}{\sqrt2}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-0a80153039534180e29c7a3a16700a3c_l3.png)
Q.15: If , then what will be the value of
?
(A)
(B)
(C)
(D)
Show Answer
![Rendered by QuickLaTeX.com \frac{\sqrt{41}}{4}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-29a9e6d5dbc5b2726978c4b3e646c450_l3.png)
![](https://sscstudy.com/wp-content/uploads/2021/12/image-26.png)
Q.16: The value of is:
(A)
(B)
(C) 1
(D) 0
Show Answer
![Rendered by QuickLaTeX.com \frac{1}{\sqrt3}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-515c6ea43e33df7e16982f1c00b4b345_l3.png)
Cos 8o Cos 82o = 1
Cos 24o Cos 60o = 1
Sin 82o Sin 8o = 1
Sin 66o Sin 24o = 1
so
![Rendered by QuickLaTeX.com \frac{Cos 66^o}{Sin 60^o}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-4e60bf31f452b9a2d1f5a98deb3b3630_l3.png)
![Rendered by QuickLaTeX.com Cot 60=\frac{1}{\sqrt3}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-3c692e24c4310077be2ea3f904be6f1f_l3.png)
Q.17: If Sin B = , then what is the value of Cot B, where 0o <B<90o ?
(A)
(B)
(C)
(D)
Show Answer
![Rendered by QuickLaTeX.com \frac{40}{9}](https://sscstudy.com/wp-content/ql-cache/quicklatex.com-358a0b847fc46a46e2afe44d888fce26_l3.png)
![](https://sscstudy.com/wp-content/uploads/2021/12/image-24.png)
Q.18: If , then the value of
will be equal to:
(A) 36
(B) 100
(C) 18
(D) 72
Show Answer
![](https://sscstudy.com/wp-content/uploads/2021/12/image-29.png)
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