Is 3+cos(2y)=2+2cos^2(y) ?

The answer to whether 3+cos(2y)=2+2cos^2(y) is True

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prove 3+cos(2y)=2+2cos^2(y)

prove

3 + cos (2 y) = 2 + 2 cos^{2} (y)

True

Solution steps

3 + cos (2 y) = 2 + 2 cos^{2} (y)

Manipulating left side

3 + cos (2 y)

Rewrite using trig identities

3 + cos (2 y)

Use the Double Angle identity:

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

= 3 + 2 cos^{2} (y) - 1

Simplify

3 + 2 cos^{2} (y) - 1 : 2 cos^{2} (y) + 2

3 + 2 cos^{2} (y) - 1

Group like terms

= 2 cos^{2} (y) + 3 - 1

Add/Subtract the numbers:

3 - 1 = 2

= 2 cos^{2} (y) + 2

= 2 cos^{2} (y) + 2

= 2 cos^{2} (y) + 2

= 2 + 2 cos^{2} (y)

We showed that the two sides could take the same form

\Rightarrow True

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