Question

if A and B are acute angles such that sinA=cosB,prove that(A+B)=90°​

Answer 1

Answer:hello

Step-by-step explanation:as we know that

sin theta =cos90-theta

here

sina =cos 90-a

this means

sina = cos b

here we can say that

sina = sin90-b

sin now cancelled we get

a=90-b

taking this side we get

a+B =90

hence proved

hope this helps

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.