Question

If $\tan \Theta =\frac{3}{4}and0<\Theta ,<{90}^{\circ }$ , then the value of $\sin \Theta \cos \Theta$ is

• A. $\frac{1}{5}$
• B. $\frac{9}{5}$
• C. $\frac{12}{25}$
• D. $\frac{25}{12}$

Answer 1

The correct option is C $\frac{12}{25}$

Given $\tan \theta =\frac{3}{4}$
$\therefore \sec \theta =\sqrt{1+{\tan }^2\theta }$
$=\sqrt{1+\frac{9}{16}}=\sqrt{\frac{25}{16}}=\frac{5}{4}$
or $\cot \theta =\frac{4}{5}$
$\therefore \sin \theta \cos \theta =\tan \theta .{\cos }^2\theta$
$=\frac{3}{4}\times \frac{16}{25}=\frac{12}{25}$