Question

If a and b are acute angles and sina=cosb prove that a+b=90

Answer 1

Answer:

we can write Sina as cos(90-a)

so the eqn. become

cos(90-a) = cos(b)

90-a = b

90 = a+b

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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.