if sin theta - cos theta =3/5 then sin theta.cos theta =?
Answers
Answered by
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
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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