If sin A = \frac{3}{5} and A lies in the quadrant, what is the value of Tan A?
If sin A = \frac{3}{5} and A lies in the quadrant, what is the value of Tan A?
यदि sin A = $ \frac{3}{5}$ और A दुसरे चतुर्थाश में स्थित है, तो tan A का मान क्या हैं?
Detailed Solution & Logic
Correct Answer:
$ \frac{3}{4}$
Given:
$\sin A = \frac{3}{5}$ and A is in second quadrant
Using identity:
$\sin^2 A + \cos^2 A = 1$
$\cos^2 A = 1 - \left(\frac{3}{5}\right)^2 = 1 - \frac{9}{25} = \frac{16}{25}$
$\cos A = \frac{4}{5}$
But in second quadrant, $\cos A$ is negative
So,
$\cos A = -\frac{4}{5}$
Now,
$\tan A = \frac{\sin A}{\cos A}$
$= \frac{\frac{3}{5}}{-\frac{4}{5}} = -\frac{3}{4}$
Final Answer: $-\frac{3}{4}$ ✅
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