Quantitative Aptitude Ques 432

Question: If A, B and C are the angles of a $ \Delta ABC, $ then following is equal to $ ( \frac{B+C}{2} ) $

Options:

A) $ cosec\frac{A}{2} $

B) $ \cos \frac{A}{2} $

C) $ \sec \frac{A}{2} $

D) $ \sec \frac{B}{2} $

Show Answer

Answer:

Correct Answer: B

Solution:

  • A, B and C are angles of a triangle.

$ \therefore $ $ \angle A+\angle B+\angle C=180{}^\circ $ $ \sin ( \frac{B+C}{2} )=\sin ( \frac{A+B+C}{2}-\frac{A}{2} ) $ $ =\sin ( 90{}^\circ -\frac{A}{2} )=\cos \frac{A}{2} $

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