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

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

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

prove

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

True

Solution steps

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

Manipulating left side

cos (2 a)

Rewrite using trig identities

= cos^{2} (a) - sin^{2} (a)

Use the Pythagorean identity:

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

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

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

Simplify

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

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

We showed that the two sides could take the same form

\Rightarrow True

sec^{2} (x) - tan^{2} (x) = tan (x) cot (x)

\frac{tan ( θ )}{tan ( θ ) - 1} = \frac{1}{1 - cot ( θ )}

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

2 cos (x) tan (x) csc (x) = 2

sec^{2} (y) - cot^{2} (\frac{π}{2} - y) = 1