question_answer

If \[\tan \theta =\frac{3}{4}\] and \[0<\theta <90{}^\circ ,\] then \[\sin \theta \cdot \cos \theta \]is equal to

A) \[\frac{12}{25}\]                       

B) \[\frac{3}{5}\]

C) \[\frac{18}{25}\]                                   

D) \[\frac{4}{5}\]

Correct Answer: A

Solution :

\[\tan \theta =\frac{3}{4}\,\,\Rightarrow \,\,\sin \theta =\frac{3}{5}\]

and \[\cos \theta =\frac{4}{5}\]

\[\Rightarrow \] \[\sin \theta \cos \theta =\frac{12}{25}\]