Is 2cos^2(A)=1+cos(2A) ?

The answer to whether 2cos^2(A)=1+cos(2A) is True

prove 2cos^2(A)=1+cos(2A)

prove

2 cos^{2} (A) = 1 + cos (2 A)

True

Solution steps

2 cos^{2} (A) = 1 + cos (2 A)

Manipulating right side

1 + cos (2 A)

Rewrite using trig identities

1 + cos (2 A)

Use the Double Angle identity:

cos (2 x) = 2 cos^{2} (x) - 1

= 1 + 2 cos^{2} (A) - 1

Simplify

1 + 2 cos^{2} (A) - 1 : 2 cos^{2} (A)

1 + 2 cos^{2} (A) - 1

Group like terms

= 2 cos^{2} (A) + 1 - 1

1 - 1 = 0

= 2 cos^{2} (A)

= 2 cos^{2} (A)

= 2 cos^{2} (A)

We showed that the two sides could take the same form

\Rightarrow True

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