Question

How do you verify the identity (1+siny)(1+sin(−y))=cos2y?

Answer 1

HELLO MATE!

TAKING L.H.S

= (1+sin y) (1+sin (-y)

= (1+sin y) (1-sin y)

Using identity (a-b) (a+b)= a^2 -b^2

= (1)^2-(sin y)^2

= 1^2 - sin y^2

now, using identity 1^2 -sin theta^2 = cos theta^2

we get LHS as

= cos y^2

and R.H.S. is cos y^2

HENCE THEY ARE PROVED EQUAL!

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