Question

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

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

Answer 1

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

We have,

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

$\Rightarrow \frac{1+\frac{{\sin }^2\theta }{{\cos }^2\theta }}{1+\frac{{\cos }^2\theta }{{\sin }^2\theta }}$

$\Rightarrow \frac{\frac{{\cos }^2\theta +{\sin }^2\theta }{{\cos }^2\theta }}{\frac{{\sin }^2\theta +{\cos }^2\theta }{{\sin }^2\theta }}$

$\Rightarrow \frac{{\sin }^2\theta }{{\cos }^2\theta }$

$\Rightarrow {\tan }^2\theta$

Hence, this is the answer.