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

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

Popular >

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 (2 t)

Rewrite as

= sin (t + t)

Use the Angle Sum identity:

sin (s + s) = sin (s) cos (s) + cos (s) sin (s)

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

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

Simplify

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

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

Add similar elements:

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

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

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

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