Question

If cos $\theta =\frac{3}{5},$ then the value of $\frac{\sin \theta \tan \theta +1}{2{\tan }^2\theta }$ is

• A. $\frac{88}{160}$
• B. $\frac{91}{160}$
• C. $\frac{92}{160}$
• D. $\frac{93}{160}$

Answer 1

The correct option is D $\frac{93}{160}$

$Givencos\theta =\frac{3}{5}\therefore sin\theta =\sqrt{1-co{s}^2\theta }=\sqrt{1-{\left(\frac{3}{5}\right)}^2}=\frac{4}{5}\therefore tan\theta =\frac{4}{5}÷\frac{3}{5}=\frac{4}{3}Now,\frac{sin\theta tan\theta +1}{{2tan}^2\theta }=\frac{\frac{4}{5}\times \frac{4}{3}+1}{2\times \frac{4}{3}\times \frac{4}{3}}=93/160$