Is tan(θ)sin(2θ)=2-2cos^2(θ) ?

The answer to whether tan(θ)sin(2θ)=2-2cos^2(θ) is True

Popular >

prove tan(θ)sin(2θ)=2-2cos^2(θ)

prove

tan (θ) sin (2 θ) = 2 - 2 cos^{2} (θ)

True

Solution steps

tan (θ) sin (2 θ) = 2 - 2 cos^{2} (θ)

Manipulating left side

tan (θ) sin (2 θ)

Express with sin, cos

= \frac{sin ( 2 θ ) sin ( θ )}{cos ( θ )}

Rewrite using trig identities

= 2 (1 - cos^{2} (θ))

Expand

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

= 2 - 2 cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

- 30 cos (3 x) sin (3 x) = - 15 sin (6 x)

2 sin^{2} (θ) - 1 = sin^{4} (θ) - cos^{4} (θ)

csc (2 θ) = \frac{1 + cot ^{2} ( θ )}{2 cot ( θ )}

csc^{4} (θ) - cot^{4} (θ) = 2 cot^{2} (θ) + 1

sec (b) cot (b) = csc (b)

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