Question

vii)
cos (x+y).cos (x-y) = cos²y - sin²x​

Answer 1

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Answer:

Cos(x + y)Cos(x - y) = Cos²y - Sin²x

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 .