Is sin(3x)=(sin(x))(3-4sin^2(x)) ?

The answer to whether sin(3x)=(sin(x))(3-4sin^2(x)) is True

Popular >

prove sin(3x)=(sin(x))(3-4sin^2(x))

prove

sin (3 x) = (sin (x)) (3 - 4 sin^{2} (x))

True

Solution steps

sin (3 x) = sin (x) (3 - 4 sin^{2} (x))

Manipulating left side

sin (3 x)

Rewrite using trig identities

= 3 sin (x) - 4 sin^{3} (x)

Factor

3 sin (x) - 4 sin^{3} (x) : sin (x) (3 - 4 sin^{2} (x))

= (3 - 4 sin^{2} (x)) sin (x)

= sin (x) (3 - 4 sin^{2} (x))

We showed that the two sides could take the same form

\Rightarrow True

sec (a) + tan (a) = \frac{1}{sec ( a )} + tan (a)

cos (3 a) = 4 cos^{3} (a) - 3 cos (a)

2 cos (x) sin (y) = sin (x + y) - sin (x - y)

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

\frac{tan ( 2 x ) + cot ( 2 x )}{csc ( 2 x )} = sec (2 x)

Is sin(3x)=(sin(x))(3-4sin^2(x)) ?
The answer to whether sin(3x)=(sin(x))(3-4sin^2(x)) is True