Is prove-30cos(3x)sin(3x)=-15sin(6x) ?

The answer to whether prove-30cos(3x)sin(3x)=-15sin(6x) is True

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

prove

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

True

Solution steps

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

Manipulating left side

- 30 cos (3 x) sin (3 x)

Rewrite using trig identities

- 30 cos (3 x) sin (3 x)

= - 15 \cdot 2 cos (3 x) sin (3 x)

Use the Double Angle identity:

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

= - 15 sin (2 \cdot 3 x)

Simplify

= - 15 sin (6 x)

= - 15 sin (6 x)

We showed that the two sides could take the same form

\Rightarrow True

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)

\frac{1 - cos ( 2 θ )}{sin ( 2 θ )} = tan (θ)

Is prove-30cos(3x)sin(3x)=-15sin(6x) ?
The answer to whether prove-30cos(3x)sin(3x)=-15sin(6x) is True