How do you use a double angle formula to rewrite the expression #(cosx+sinx)(cosx-sinx)#?

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Answer 1 · 2017-03-03T06:56:47

#(cosx+sinx)(cosx-sinx)=cos2x#

Recall #cos2A=2cos^2A-1=1-2sin^2A=cos^2A-sin^2A# or #cos(A+B)=cosAcosB-sinAsinB#.

Now as #(a+b)(a-b)=a^2-b^2#

#(cosx+sinx)(cosx-sinx)#

= #cos^2x-sin^2x#

= #cosxcosx-sinxsinx#

= #cos(x+x)#

= #cos2x#