Question

if sinA=cosB,prove that A+B=90°​

Answer 1

Answer:

it is obvious

Step-by-step explanation:

If SinA=CosB

1\√2=1\√2

∴ A = 45° , B = 45°

A + B = 90°

Answer 2

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.