Question

$1 + \sec^2 x \cdot \sin^2 x = $

• A. $\sin 2x$
• B. $\sin^2 x$
• C. $\tan^2 x$
• D. $\sec^2 x$

Hint:

Use basic trigonometric identities to transform expressions involving $\sec$, $\tan$, and $\sin$.

Answer 1

The Correct Option is D

We know that $\tan x = \dfrac{\sin x}{\cos x}$ and $\sec x = \dfrac{1}{\cos x}$
So, $\sec^2 x \cdot \sin^2 x = \dfrac{1}{\cos^2 x} \cdot \sin^2 x = \tan^2 x$
Now, $1 + \tan^2 x = \sec^2 x$
Hence, $1 + \sec^2 x \cdot \sin^2 x = \sec^2 x$