Question

If $\theta$ is acute angle, and $tan\theta$ =$\frac{1}{\sqrt{7}}$, then $\frac{cose{c}^2\theta -se{c}^2\theta }{cose{c}^2\theta +se{c}^2\theta }=$

• A. 3/4
• B. 1/2
• C. 2
• D. 5/4

Answer 1

The correct option is A

3/4

$tan\theta =\frac{1}{\sqrt{7}}\Rightarrow cot\theta =\sqrt{7}givenexpression=\frac{co{t}^2\theta -ta{n}^2\theta }{2+co{t}^2\theta +ta{n}^2\theta }=\frac{7-\frac{1}{7}}{2+7+\frac{1}{7}}=\frac{3}{4}$