Question

If in a triangle abc, sin a = cos b then the value of cos c is

Answer 1

The answer is cos c = 0

In trigonometric function of a triangle, the angles are usually considered as acute angles of a right triangle.

Sin of an angle = opposite side/hypotenuse

Cos of an angle = adjacent side/hypotenuse

Since the question says that sin a = cos b, it means that sides a and b are opposite sides.

Therefore, the side c should be at right angle in the right triangle, i.e. c = 90

Thus, by following the standard trigonometric values, cos 90 = 0.

Answer 2

sin a = cos b

sin a = sin (90-b)

a =90-b

a+b =90,

From angle sum property, we know that

In a triangle, a + b + c =180

90+c =180

c =90°.

Now cos90° = 0.

Therefore, cosc =0