Question

If ${\sec }^2\theta +{\tan }^2\theta =3$ then find the value of $\cot \theta$.

• (A) 0
• (B) 1
• (C) 2
• (D) $\sqrt{3}$

Answer 1

The Correct Option is B

Explanation:
Given,${\sec }^2\theta +{\tan }^2\theta =3$...(i)Subtracting 1 from both sides in equation (i) we get,${\sec }^2\theta +{\tan }^2\theta -1=3-1$$(\because$${\sec }^2\theta -1={\tan }^2\theta )$$\Rightarrow {\tan }^2\theta +{\tan }^2\theta =2$$\Rightarrow 2{\tan }^2\theta =2$$\Rightarrow {\tan }^2\theta =1$$\Rightarrow \tan \theta =1$Now,$\cot \theta =\frac{1}{\tan \theta }$$=1$Hence, the correct option is (B).