question_answer

If \[\theta \] lies in the second quadrant arid \[3\tan \theta +4=0,\] then the value of \[\sin \theta +\cos \theta \] is equal to

A)  \[\frac{1}{5}\]                 

B)  \[\frac{2}{5}\]

C)  \[\frac{3}{5}\]

D)  \[\frac{4}{5}\]

Correct Answer: A

Solution :

Given,  \[3\tan \theta +4=0\] \[\Rightarrow \] \[\tan \theta =-\frac{4}{3}\] Since, \[\theta \] lies in IInd quadrant. \[\therefore \] \[\sin \theta =\frac{4}{5}\] and \[\cos \theta =\frac{-3}{5}\] \[\therefore \] \[\sin \theta +\cos \theta =\frac{4}{5}-\frac{3}{5}=\frac{1}{5}\]