Question #923f4

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Answer 1 · 2017-03-23T02:08:12

I tried this:

If you multiply the brackets you get:

#1cancel(+sin(x))cancel(-sin(x))-sin^2(x)=cos^2(x)#

#1-sin^2(x)=cos^2(x)# that it is true;

remembering the fundamental identity:
#sin^2(x)+cos^2(x)=1#

Answer 2 · 2017-03-24T00:56:07

#"Given: "(1-sinx)(1+sinx)=cos^2x#

#"LHS"=(1-sinx)(1+sinx)#

#=1+sinx-sinx-sin^2x#

#=1-sin^2x#

Use the Pythagorean identity: #color(blue)(sin^2x+cos^2x=1)#

#color(blue)(cos^2x=1-sin^2x)#

#"LHS"=cos^2x#

#"QED"#