Is (sin(2θ))/(sin(θ))=2cos(θ) ?

The answer to whether (sin(2θ))/(sin(θ))=2cos(θ) is True

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prove (sin(2θ))/(sin(θ))=2cos(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{sin ( 2 θ )}{sin ( θ )}

Rewrite using trig identities

\frac{sin ( 2 θ )}{sin ( θ )}

Use the Double Angle identity:

sin (2 x) = 2 sin (x) cos (x)

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

Cancel the common factor:

sin (θ)

= 2 cos (θ)

= 2 cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

81 - 9 (3 sin (x))^{2} = 1

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

\frac{tan ^{2} ( t )}{sec ( t )} = sec (t) - cot (t)

81 - 9 (3 sin (x))^{2} = 9 cos (x)

25 tan^{2} (5 x) + 25 = 25 + (5 tan (5 x))^{2}

Is (sin(2θ))/(sin(θ))=2cos(θ) ?
The answer to whether (sin(2θ))/(sin(θ))=2cos(θ) is True