If cosec A-sinA = 2, then find the value of sinA.
If cosec A-sinA = 2, then find the value of sinA.
cosecA-sinA = 2, तो sinA का मान ज्ञात कीजिए
Detailed Solution & Logic
Correct Answer:
$- 1 + \sqrt{2} $
Solution:
Let $\sin A = x$.
Given,
$\csc A - \sin A = 2$
$\frac{1}{x} - x = 2$
$\frac{1-x^2}{x} = 2$
$1 - x^2 = 2x$
$x^2 + 2x - 1 = 0$
$\Rightarrow x = \frac{-2 \pm \sqrt{4+4}}{2} = -1 \pm \sqrt{2}$
Since $\sin A$ must lie between $-1$ and $1$,
$\sin A = -1 + \sqrt{2}$
(The other value $-1-\sqrt{2}$ is not possible.)
Answer: $ -1+\sqrt{2}$
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