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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sin (2 x + x)

Rewrite as

= sin (3 x)

Rewrite using trig identities

= sin (3 x)

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

We showed that the two sides could take the same form

\Rightarrow True

sin (3 x) = 2 \cdot sin (\frac{3 x}{2}) \cdot cos (\frac{3 x}{2})

(sec (a) - tan (a)) (csc (a) + 1) = cot (a)

- cos (x) sin^{2} (x) = - cos (x) (sin (x))^{2}

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

6 sin (\frac{5 π}{6}) = 2 + 2 sin (\frac{5 π}{6})

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