Question

Choose the correct answer from the alternatives given.
If sec $\theta$+ tan $\theta$ = 2+$\sqrt{5}$ then the value of sin $\theta$ is

• A. $\frac{2}{\sqrt{5}}$
• B. $\frac{1}{\sqrt{5}}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{4}{5}$

Answer 1

Answer: (A)

$\frac{2}{\sqrt{5}}$

$sec\theta +tan\theta =2\sqrt{5}$
$sec\theta -tan\theta =\frac{1}{2+\sqrt{5}}=\frac{1}{\sqrt{5}+2}\times \frac{\sqrt{5}-2}{\sqrt{5}-2}=\sqrt{5}-2$
$sec\theta =\sqrt{5}\Rightarrow cos\theta =\frac{1}{\sqrt{5}}$
$se{n}^2\theta =1-co{s}^2\theta =1-\left(\frac{1}{\sqrt{5}}\right)=1-\frac{1}{5}=\frac{4}{5}\Rightarrow sin\theta =\frac{2}{\sqrt{5}}$