Question

Prove that: (1 - sino + coso)2 = 2(1 + cos0)(1 – sino)​

Answer 1

Step-by-step explanation:

we have to prove :

(1-sinΦ+cosΦ)²=2(1+cosΦ)(1-sinΦ)

we know , (a+b+c)² = a²+ b²+ c² + 2ab + 2bc + 2ca

therefore, LHS =

(1-sinΦ+cosΦ)² = (1+(-sinΦ)+cosΦ)²

=1+sin²Φ+cos²Φ-2sinΦ-2sinΦ.cosΦ+2cosΦ

= 1+1--2sinΦ+2cosΦ-2sinΦ.cosΦ

=2-2sinΦ+2cosΦ(1-sinΦ)

=2(1-sinΦ)+2cosΦ(1-sinΦ)

=(2+2cosΦ)(1-sinΦ)

=2(1+cosΦ)(1-sinΦ) = RHS

Hence proved.