Is cos(4θ)=2(cos(2θ))^2-1 ?

The answer to whether cos(4θ)=2(cos(2θ))^2-1 is True

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prove cos(4θ)=2(cos(2θ))^2-1

prove

cos (4 θ) = 2 (cos (2 θ))^{2} - 1

True

Solution steps

cos (4 θ) = 2 (cos (2 θ))^{2} - 1

Manipulating left side

cos (4 θ)

Rewrite as

= cos (2 \cdot 2 θ)

Use the Double Angle identity:

cos (2 θ) = 2 cos^{2} (θ) - 1

cos (2 \cdot 2 θ) = 2 cos^{2} (2 θ) - 1

= 2 cos^{2} (2 θ) - 1

We showed that the two sides could take the same form

\Rightarrow True

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

tan (\frac{x}{2}) = - cot (x) + csc (x)

\frac{1}{csc ^{2} ( x )} + \frac{1}{sec ^{2} ( x )} = 1

cot (\frac{5 π}{12}) = 2 - 3

cos (4 x) = cos^{2} (2 x) - sin^{2} (2 x)

Is cos(4θ)=2(cos(2θ))^2-1 ?
The answer to whether cos(4θ)=2(cos(2θ))^2-1 is True