Question

If A,B  are acute angles such that sinA=cosB, then A+B=​

Answer 1

Answer:

A+B = 90°

Step-by-step explanation:

Given,

If A,B are acute angles,

sinA = cosB

sinA = sin(90°-B)

A = 90°-B

A+B = 90°

:. A+B = 90°.

Answer 2

Given :

• sin A = cos B

To Find :

• A + B = ?

Solution :

We are given,

sin A = cos B

Now, we know that,

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

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

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

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

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

Therefore, A + B = 90°