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

cos (b) csc (b) tan (b) = 1

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

tan^{6} (x) = tan^{4} (x) sec^{2} (x) - tan^{4} (x)

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

cos (2 x) = cos (x + x)