Is 2cot^2(A)sin^2(A)=1+cos(2A) ?

The answer to whether 2cot^2(A)sin^2(A)=1+cos(2A) is True

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prove 2cot^2(A)sin^2(A)=1+cos(2A)

prove

2 cot^{2} (A) sin^{2} (A) = 1 + cos (2 A)

True

Solution steps

2 cot^{2} (A) sin^{2} (A) = 1 + cos (2 A)

Manipulating left side

2 cot^{2} (A) sin^{2} (A)

Express with sin, cos

= 2 cos^{2} (A)

Rewrite using trig identities

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

Expand

(1 - sin^{2} (A)) \cdot 2 : 2 - 2 sin^{2} (A)

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

Rewrite using trig identities

= cos (2 A) + 1

= 1 + cos (2 A)

We showed that the two sides could take the same form

\Rightarrow True

sin (x) + cos (x) = cos (x) (1 + tan (x))

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

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

2 cos (x - \frac{π}{4}) = cos (x) + sin (x)

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

Is 2cot^2(A)sin^2(A)=1+cos(2A) ?
The answer to whether 2cot^2(A)sin^2(A)=1+cos(2A) is True