Is 2(1-sin^2(x))=cos(2x)+1 ?

The answer to whether 2(1-sin^2(x))=cos(2x)+1 is True

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prove 2(1-sin^2(x))=cos(2x)+1

prove

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

True

Solution steps

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

Manipulating right side

cos (2 x) + 1

Rewrite using trig identities

cos (2 x) + 1

Use the Double Angle identity:

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

= 1 - 2 sin^{2} (x) + 1

Simplify

1 - 2 sin^{2} (x) + 1 : - 2 sin^{2} (x) + 2

1 - 2 sin^{2} (x) + 1

Group like terms

= - 2 sin^{2} (x) + 1 + 1

Add the numbers:

1 + 1 = 2

= - 2 sin^{2} (x) + 2

= - 2 sin^{2} (x) + 2

= - 2 sin^{2} (x) + 2

Factor

2 - 2 sin^{2} (x) : 2 (1 - sin^{2} (x))

2 - 2 sin^{2} (x)

Rewrite as

= 2 \cdot 1 - 2 sin^{2} (x)

Factor out common term

2

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

= (1 - sin^{2} (x)) \cdot 2

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

We showed that the two sides could take the same form

\Rightarrow True

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tan (1 5^{\circ}) = tan (4 5^{\circ} - 3 0^{\circ})

Is 2(1-sin^2(x))=cos(2x)+1 ?
The answer to whether 2(1-sin^2(x))=cos(2x)+1 is True