Question

If A,B are acute angle such that sinA=cosB then A+B=
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Answer 1

Answer:

90° is the answer

Step-by-step explanation:

since only one value of sin and cos satisfies the given condition which is sin 45 and cos 45 . summing 45 and 45 gives 90° as the answer.

OR

since we know that angle A and B are acute angle. angle C is 90° so according to angle sum property of triangle A+B=90°

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hope it helped you.

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°