^2 +cosec^2 = ? - Vidyadip

MCQ

$\sec ^2 \theta+\operatorname{cosec}^2 \theta=$ ?

✓
$\sec ^2 \theta \operatorname{cosec}^2 \theta$
B
$\sin ^2 \theta \cdot \cos ^2 \theta$
C
$1$
D
None of these

✓

Answer

Correct option: A.

$\sec ^2 \theta \operatorname{cosec}^2 \theta$

$\sec ^2 \theta+\operatorname{cosec}^2 \theta$
$=\frac{1}{\cos ^2 \theta}+\frac{1}{\sin ^2 \theta}$
$=\frac{\sin ^2 \theta+\cos ^2 \theta}{\sin ^2 \theta \cdot \cos ^2 \theta}$
$=\frac{1}{\sin ^2 \theta \cdot \cos ^2 \theta}{\left[\because \sin ^2 \theta+\cos ^2 \theta=1\right]}$
$=\frac{1}{\cos ^2 \theta} \times \frac{1}{\sin ^2 \theta}$
$=\sec ^2 \theta \cdot \operatorname{cosec}^2 \theta .$

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