If tan A = 3/4, then sin A cos A = 12/25. Prove the following statement

Solution:

It is given that

tan A = 3/4 = Perpendicular/ Base

Consider P = 3k and B = 4k

Using the Pythagorean Theorem

Hypotenuse² = Perpendicular² + Base²

Hypotenuse² = (3k)² + (4k)²

= 9k² + 16k²

= 25k²

So Hypotenuse = 5k

We know that

sin A = Perpendicular/ Hypotenuse

= 3k/5k

= 3/5

cos A = Base/ Hypotenuse

= 4k/5k

= 4/5

sin A. cos A = 3/5 . 4/5 = 12/25

Therefore, it is proved.

✦ Try This: If cosec A + sec A = cosec B + sec B, prove that tan A . tan B = cot (A + B)/2.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8

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NCERT Exemplar Class 10 Maths Exercise 8.3 Problem 3

If tan A = 3/4, then sin A cos A = 12/25. Prove the following statement

Summary:

Trigonometric ratios can be calculated by taking the ratio of any two sides of the right-angled triangle. It is proved that sin A cos A = 12/25 if tan A = 3/4

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