Question #8ea5f

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Answer 1 · 2018-02-06T18:25:53

Kindly refer to a Proof in the Explanation.

We have, #1+cos2x=1+cos(x+x)#.

Expanding #cos(x+x)# with the help of,

#cos(A+B)=cosAcosB-sinAsinB#, we have,

# 1+color(red)(cos2x)=1+color(red)(cosxcosx-sinxsinx)#,

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

#=color(blue)(cos^2x)+cos^2x#.

# rArr 1+cos2x=2cos^2x#.