How do you verify #(1-cos^2y + sin^2y)^2 + 4 sin^2y cos^2y= 4 sin^2y#?

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Answer 1 · 2016-04-17T02:10:27

See below

LHS =left hand side, RHS =right hand side

LHS #=((1-cos ^2y)+sin^2y)^2+4sin^2ycos^2y#

#=(sin^2y+sin^2y)^2 +4 sin^2y cos^2 y#

#=(2sin^2y)^2+4 sin^2y cos^2 y#

#=4sin^4y+4sin^2ycos^2y#

#=4sin^2y(sin^2y+cos^2y)#

#=4 sin^2y * 1#

#=4 sin^2y#

#=RHS #