Question

Cos x + cos y the whole square + sin x minus sin y the whole square is equal to 4 cos square x + y divided 2

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

(Cosx + Cosy)² + (Sinx + Siny)² = 4(Cos²((x - y)/2))

Step-by-step explanation:

prove that cos x + cos y whole square + sin x + sin y whole square equal to 4 cos square x minus y upon 2​

(Cosx + Cosy)² + (Sinx + Siny)² = 4(Cos²((x - y)/2))

LHS

= Cos²x + Cos²y + 2CosxCosy  + Sin²x + Sin²y + 2SinxSiny

= 1 + 1 + 2CosxCosy + 2SinxSiny

= 1 + 1 + 2(CosxCosy + SinxSiny )

= 2 + 2Cos(x -y)

= 2 ( 1 + cos(x-y))

= 2 ( 2Cos²((x-y)/2))

= 4Cos²((x-y)/2)

= RHS

(Cosx + Cosy)² + (Sinx + Siny)² = 4(Cos²((x - y)/2))