10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

If \[\sin A=\cos B=\frac{1}{2},\]then the value of \[\tan \frac{1}{2}(A+B)\] is:

A) \[0\]

B) \[1\]

C) \[\sqrt{3}\]

D) \[\infty \]

Correct Answer: B

Solution :

[b] Given, \[\sin A=\frac{1}{2}=\sin 30{}^\circ \]

\[\Rightarrow \,\,\,\,\,\,\,\,\,A=30{}^\circ \]

and\[\cos B=\frac{1}{2}=\cos 60{}^\circ \]

\[\Rightarrow \,\,\,\,\,\,\,\,B=60{}^\circ \]

\[\therefore \,\,\,\,\,\,\tan \frac{1}{2}(A+B)=\tan \frac{1}{2}(30{}^\circ +60{}^\circ )=\tan 45{}^\circ =1\]