Question

Prove:

If tan A = 3/4 , then sin A cos A = 12/25

Answer 1

According to the question,

tan A = ¾

We know,

tan A = perpendicular/ base

So,

tan A = 3k/4k

Where,

Perpendicular = 3k

Base = 4k

Using Pythagoras Theorem,

(hypotenuse)² = (perpendicular)² + (base)²

(hypotenuse)² = (3k)²+ (4k)² = 9k²+16k² = 25k²

hypotenuse = 5k

To find sin A and cos A,

Hence, proved.