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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 sin^{2} (x)

Rewrite using trig identities

2 sin^{2} (x)

Use the Double Angle identity:

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

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

= - (cos (2 x) - 1)

Simplify

- (cos (2 x) - 1) : - cos (2 x) + 1

- (cos (2 x) - 1)

Distribute parentheses

= - (cos (2 x)) - (- 1)

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - cos (2 x) + 1

= - cos (2 x) + 1

= - cos (2 x) + 1

= 1 - cos (2 x)

We showed that the two sides could take the same form

\Rightarrow True

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

2 sin (4 x) = 4 sin (2 x) cos (2 x)

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

\frac{1}{cos ^{2} ( x )} = (\frac{1}{cos ( x )})^{2}

\frac{tan ( x )}{1 + tan ^{2} ( x )} = sin (x) cos (x)