Question

When simplified the trigonometric expression
$\frac{1+{\sin }^2\theta {\sec }^2\theta }{1+{\cos }^2\theta {\csc }^2\theta }$ reduces to______________.

• A. $\sin \theta$
• B. $\cos \theta$
• C. ${\cot }^2\theta$
• D. ${\tan }^2\theta$

Answer 1

The correct option is D ${\tan }^2\theta$

Given Exp. $=\frac{1+si{n}^2\theta se{c}^2\theta }{1+co{s}^2\theta cs{c}^2\theta }$

$=\frac{1+ta{n}^2\theta }{1+co{t}^2\theta }=\frac{se{c}^2\theta }{cs{c}^2\theta }$

$=\frac{si{n}^2\theta }{co{s}^2\theta }=ta{n}^2\theta$