Question

plzzzzzzzz try to an this question .....we have to prove the given question ​

Answer 1

I am taking alpha as x and beta as y for convenience :3

Now onto the question,

cosy cos(2x-y) = cos²x -sin²(x-y)

Taking RHS first,

cos²x-sin²(x-y)

we know, by identity,

cos²a - sin²b = cos(a-b)cos(a+b)

Now, putting this identity in use in RHS we get,

cos²x - sin²(x-y)

=>cos(x-(x-y)) cos(x+x+y)

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

=>cos y cos(2x+y) = LHS

Cheers!