Question

Prove the followings identities:
(1 + cos θ)(1 – cos θ) = sin2θ

Answer 1

Answer:

[1+cosФ][1-cosФ]=sin²Ф

1-cosФ+cosФ-cos²Ф=sin²Ф

1-cos²Ф=sin²Ф

∴sin²Ф=sin²Ф

HENCE PROVED

Answer 2

since sin2(X)= 2sinx.cosx

so

(1+cos(x)) (1-cos(x)) = sin2(x)

we know that. (a+b)(a-b) = a²-b²

using this formula our formula becomes

(1+cos(x)) (1-cos(x)) = 1²-cos²(x)

since we know that 1-cos²(x) = sin²(x)

1²=1

our formula becomes

1-cos²(x)

LHS=RHS