Question

If sinA=cosB then prove that A+B=90°

Answer 1

given that sinA = cosB ....(1)

we know that cosB= sin(90°-B), we write (1) as

sinA =sin(90°-B)

if A,B are acute angles , then A=90°-B

--->A+B=90°.

Answer 2

Given,

Sin A = Cos B

To find,

We have to prove that A+B=90°.

Solution,

We can simply prove the given condition i.e. A+B=90° by using the transformation formulas of trigonometry.

As we know, Cos B = Sin (90-B)

Substituting Sin (90-B) in place of Cos B, we get

Sin A = Sin (90-B)

Taking inverse both sides, we get

Sin⁻¹ Sin A = Sin⁻¹ Sin (90-B)

A = 90-B

Shifting B to LHS, we get

A+B = 90°

Hence, proved that if sinA=cosB then A+B = 90°.