Question

If cos(A+B)=0and sin(A-B)= ½(where A and B are acute angles)find the measure of each angles.​

Answer 1

cos (A+B)= 0

or, cos(A+B) = cos90°. => A + B = 90°…………….(1).

sin(A-B) = 1/2.

or, sin(A-B) = sin 30°. =>. A - B. = 30°…………….(2)

Adding eqn.(1) and eqn.(2).

2.A = 120°

or, A=120°/2 = 60°. , putting A =60° in eqn.(1).

60° + B = 90°.

or, B = 90° - 60° = 30°.

A= 60°. , B=30°. Answer.