Question

8. If tan A = ¾ then show that sin A cos A =12/25.​

Answer 1

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,

sinA = 3/5

cosA= 4/5

then sinAcosA = 3/5×4/5

= 12/25

Answer 2

GIVEN:

tanA=3/4

TO PROVE:

sinA.cosA = 12/25

we know that:

tanA = perpendicular/base

so, tanA = 3k/4k

where perpendicular=3k and base=4k

USING PYTHAGORAS THEOREM:

hypotenuse^2 = perpendicular^2 + base^2

hypotenuse^2 = (3k)^2 + (4k)^2

=9k^2 + 16k^2

=25k^2

hypotenuse = 5k

TO FIND SINA AND COSA:

sinA = perpendicular/hypotenuse = 3k/5k = 3/5

cosA = base/ hypotenuse = 4k/5k = 4/5

➡multiply sinA and cosA

3/5 ×4/5 = 12/25

HENCE,PROVED