Question

if sinA=cosB then (A+B) = 90°​

Answer 1

Given :

• sin A = cos B

To Prove :

• A + B = 90°

Solution :

We are given,

sin A = cos B

Now, we know that,

$\Large \underline{\boxed{\bf{ cos \theta = sin (90^{\circ} - \theta) }}}$

$\sf : \implies sin A = sin (90^{\circ} - B)$

$\sf : \implies A = 90^{\circ} - B$

$\sf : \implies A + B = 90^{\circ}$

$\Large \underline{\boxed{\bf{A + B = 90^{\circ}}}}$

Hence, Proved.

Answer 2

Answer :-

→ sin A = cos B

→ sin A = sin ( 90 - B )

→ A = 90 - B

→ A + B = 90°

Hence proved.