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 (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

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

\frac{csc ( x )}{2 cos ( x )} = csc (2 x)

tan^{2} (u) = \frac{1 - cos ( 2 u )}{1 + cos ( 2 u )}

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

csc^{4} (x) - csc^{2} (x) = cot^{2} (+ cot^{4} (x))