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