Question

If A &B are acute angles and sin A =cos B, find the value of A + B.

Answer 1

Note;

sin@ = cos(90°- @)

cos@ = sin(90°- @)

cosec@ = sec(90°- @)

sec@ = cosec(90°- @)

tan@ = cot(90°- @)

cot@ = tan(90°- @)

We have;

=> sinA = cosB

=> sinA = sin(90°- B)

=> A = 90°- B

=> A + B = 90°

Hence,

The required value of (A+B) is 90°.