^2 1+ ^2 + ^2 1+ ^2 = - Vidyadip

MCQ

$\frac{\tan ^2 \theta}{1+\tan ^2 \theta}+\frac{\cot ^2 \theta}{1+\cot ^2 \theta}=$

✓
1
B
$2 \tan ^2 \theta$
C
$2 \cot ^2 \theta$
D
$2 \sec ^2 \theta$

✓

Answer

Correct option: A.

1

(A) 1
$\frac{\tan ^2 \theta}{1+\tan ^2 \theta}+\frac{\cot ^2 \theta}{1+\cot ^2 \theta}$
$=\frac{\tan ^2 \theta}{\sec ^2 \theta}+\frac{\cot ^2 \theta}{\operatorname{cosec}^2 \theta}$
$=\tan ^2 \theta \times \frac{1}{\sec ^2 \theta}+\cot ^2 \theta \times \frac{1}{\operatorname{cosec}^2 \theta}$
$=\frac{\sin ^2 \theta}{\cos ^2 \theta} \times \cos ^2 \theta+\frac{\cos ^2 \theta}{\sin ^2 \theta} \times \sin ^2 \theta$
$=\sin ^2 \theta+\cos ^2 \theta=1$

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