Is cos(4x)=2cos^2(2x)-1 ?

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

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prove cos(4x)=2cos^2(2x)-1

prove

cos (4 x) = 2 cos^{2} (2 x) - 1

True

Solution steps

cos (4 x) = 2 cos^{2} (2 x) - 1

Manipulating left side

cos (4 x)

Rewrite as

= cos (2 \cdot 2 x)

Use the Double Angle identity:

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

- cos (x) tan (x) = - sin (x)

\frac{sin ( 2 a )}{1 - cos ( 2 a )} = cot (a)

tan (x) cot (x) = sec (x) csc (x)

sin (x) sec (x) = \frac{1}{cos ( x ) csc ( x )}

1 + tan (x) = sec (x)