Question

cos(x+y) ×cos(x-y)=cos^2y-sin^2x​

Answer 1

Answer:

Step-by-step explanation:

Cos(x + y)Cos(x - y) = Cos²y - Sin²x

LHS

= Cos(x + y)Cos(x-y)

Using Formuls

Cos(a + b) = CosACosb + SinaSinb

Cos(a - b) = CosACosb - SinaSinb

= (CosxCosy + SinxSiny)(CosxCosy - SinxSiny)

using (a + b) (a - b) = a² - b²

= (CosxCosy)² -  (SinxSiny)²

= Cos²xCos²y -  Sin²xSin²y

= Cos²y(1 - Sin²x) - (1 - Cos²y)Sin²x

= Cos²y - Cos²ySin²x - Sin²yx + Cos²ySin²x

= Cos²y - Sin²x

= RHS

QED

Proved

Cos(x + y)Cos(x - y) = Cos²y - Sin²x