What are the formula of (1)1+cos2x(2)1−cos2x

Carina Nash

Carina Nash

Answered question

2023-01-25

What are the formula of (1)1+cos2x(2)1-cos2x.

Answer & Explanation

eyakhiwabhn

eyakhiwabhn

Beginner2023-01-26Added 6 answers

cos(a+b)=cosacosb-sinasinb
Substitute a=b=x in the above equation.
cos(x+x)=cosxcosx-sinxsinxcos2x=cos2x-sin2x
1+cos2x=1+cos2x-sin2x=sin2x+cos2x+cos2x-sin2x[sin2x+cos2x=1]=2cos2x
Thus, 1+cos2x=2cos2x
Formula for 1-cos2x.
1-cos2x=1-(cos2x-sin2x)=1-cos2x+sin2x=sin2x+cos2x-cos2x+sin2x[sin2x+cos2x=1]=2sin2x
Thus, 1-cos2x=2sin2x

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