prove that: (cos x + cos y)²+(sin x - sin y)²=4cos²(x+y)÷2
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Step-by-step explanation:
LHS
=(2cosx+y/2 cosx-y/2)²+(2cosx+y/2 sinx-y/2)²
=(4cos²x+y/2 cos²x-y/2)+(4cos²x+y/2 sinx-y/2)
=4cos²x+y/2(cos²x-y/2+sin²x-y/2)
=4cos²x+y/2
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