Question:
Prove the following trigonometric identities.
$\left(1+\cot ^{2} A\right) \sin ^{2} A=1$
Solution:
We know that, $\operatorname{cosec}^{2} A-\cot ^{2} A=1$
So,
$\left(1+\cot ^{2} A\right) \sin ^{2} A=\operatorname{cosec}^{2} A \sin ^{2} A$
$=(\operatorname{cosec} A \sin A)^{2}$
$=\left(\frac{1}{\sin A} \times \sin A\right)^{2}$
$=(1)^{2}$
$=1$
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