Math, asked by amarjitchahal1978, 8 hours ago

if sin theta - cos theta =3/5 then sin theta.cos theta =?​

Answers

Answered by XxDashingGirlxX
1

ΔABC be a right angled at B

Let ∠ACB=θ

Given that, sin θ = 3/5

AB/AC = 3/5

Let AB = 3x

then AC = 5x

In right angled ΔABC,

By Pythagoras theorem,

We get

(5x)2=(3x)2+BC2

BC2=(5x)2−(3x)2

BC2=(2x)2

BC=4x

(i) cos θ = Base/ Hypotenuse

= BC / AC

= 4x /5x

= 4/5

(ii) tan θ = perpendicular/Base

= AB/BC

= 3x/4x

=3/4

Answered by sky1000000000
2

Answer

Let, theta=x, (for typing advantage)

so,sin x - cos x= 3/5 ,

now squaring both sides

in^2(x) + cos^2(x) -2 sin x *cos x = 9/25

or, 1 - 2 sin x* cos x =9/25

or, 2 sin x * cos x

= 1– 9/25

= 16/25

Therefore, sin x* cos x = 8/25

That is, sin theta * cos theta = 8/25

hope it helps you

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