Question

Let $\theta$ be an acute angle such that ${\sec }^2\theta +{\tan }^2\theta =2$ The value of $(cose{c}^2\theta +{\cot }^2\theta )$ is

• A. 9
• B. 5
• C. 4
• D. 2

Answer 1

Answer: (B)

5

$se{c}^2\theta +{\tan }^2\theta =2$
$1+{\tan }^2\theta +{\tan }^2\theta =2$
$2{\tan }^2\theta =1$
$\tan \theta =\frac{1}{\sqrt{2}}$
Hence, $\cot \theta =\sqrt{2}$
Now, $cose{c}^2\theta +{\cot }^2\theta$
= $1+{\cot }^2\theta +{\cot }^2\theta$
= $1+2{\cot }^2\theta$
= $1+2(\sqrt{2}{)}^2$
= $1+4$
= $5$