Is sin(2t)=2sin(t)(cos(t)) ?

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

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prove sin(2t)=2sin(t)(cos(t))

prove

sin (2 t) = 2 sin (t) (cos (t))

True

Solution steps

sin (2 t) = 2 sin (t) cos (t)

Manipulating left side

sin (2 t)

Rewrite using trig identities

= sin (t) cos (t) + cos (t) sin (t)

Simplify

sin (t) cos (t) + cos (t) sin (t) : 2 sin (t) cos (t)

= 2 sin (t) cos (t)

We showed that the two sides could take the same form

\Rightarrow True

2 sin (x + 4 5^{\circ}) = sin (x) + cos (x)

4 cot (θ) = cot (θ) sin^{2} (θ)

cos (2 θ) + 1 = 2 cos^{2} (θ)

- 2 cos (x) sec^{2} (x) = - \frac{2}{cos ( x )}

1 + sin (4 a) + sin (2 a) = sin (2 a)

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