Question

Find the value of ${\cos }^2\theta (1+{\tan }^2\theta )+{\sin }^2\theta (1+{\cot }^2\theta )$.

• A. $1$
• B. $3$
• C. $2$
• D. $4$

Answer 1

Answer: (C)

$2$

we know that ,

$1+{\tan }^2\theta ={\sec }^2\theta 1+{\cot }^2\theta ={\text{cosec}}^2\theta$

Now, ${\cos }^2\theta (1+{\tan }^2\theta )+{\sin }^2\theta (1+{\cot }^2\theta )$

$={\cos }^2\theta {\sec }^2\theta +{\sin }^2\theta {\text{cosec}}^2\theta =1+1=2$

Therefore, Answer is $2$