How do you verify the identity $(1+siny)(1+sin(-y))=cos^2y$ ?

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Answer 1 · 2017-01-17T20:33:48

see below

Left Hand Side:

Use the property for odd trigonometric function: $sin(-y)=-siny$

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

$=1-sin^2y$

Now use the property $sin^2y+cos^2y=1$ and solve for $cos^2y$

$=cos^2y$

$:.=$ Right Hand Side

How do you verify the identity (1+siny)(1+sin(-y))=cos^2y(1+siny)(1+sin(-y))=cos^2y?