Question:
Prove the following trigonometric identities.
$\sin ^{2} A \cot ^{2} A+\cos ^{2} A \tan ^{2} A=1$
Solution:
We have to prove $\sin ^{2} A \cot ^{2} A+\cos ^{2} A \tan ^{2} A=1$
We know that, $\sin ^{2} A+\cos ^{2} A=1$
So,
$\sin ^{2} A \cot ^{2} A+\cos ^{2} A \tan ^{2} A=\sin ^{2} A \frac{\cos ^{2} A}{\sin ^{2} A}+\cos ^{2} A \frac{\sin ^{2} A}{\cos ^{2} A}$
$=\cos ^{2} A+\sin ^{2} A$
$=1$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.