Is 3-6sin^2(x)=3cos(2x) ?

The answer to whether 3-6sin^2(x)=3cos(2x) is True

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prove 3-6sin^2(x)=3cos(2x)

prove

3 - 6 sin^{2} (x) = 3 cos (2 x)

True

Solution steps

3 - 6 sin^{2} (x) = 3 cos (2 x)

Manipulating left side

3 - 6 sin^{2} (x)

Factor

3 - 6 sin^{2} (x) : 3 (1 - 2 sin^{2} (x))

3 - 6 sin^{2} (x)

Rewrite as

= 3 \cdot 1 - 3 \cdot 2 sin^{2} (x)

Factor out common term

3

= 3 (1 - 2 sin^{2} (x))

= (1 - 2 sin^{2} (x)) \cdot 3

Manipulating right side

3 cos (2 x)

Rewrite using trig identities

3 cos (2 x)

Use the Double Angle identity:

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

= 3 (1 - 2 sin^{2} (x))

= 3 (1 - 2 sin^{2} (x))

We showed that the two sides could take the same form

\Rightarrow True

1 + cos (2 x) = 3 sin (x)

sin^{2} (2 θ) = \frac{1 - cos ( 4 θ )}{2}

\frac{1}{tan ( x )} = arctan (x)

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

sec (- x) = \frac{1}{cos ( x )}