Is sin(2α)=2sin(α)cos(α) ?

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

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prove sin(2α)=2sin(α)cos(α)

prove

sin (2 α) = 2 sin (α) cos (α)

True

Solution steps

sin (2 α) = 2 sin (α) cos (α)

Manipulating left side

sin (2 α)

Rewrite using trig identities

sin (2 α)

Rewrite as

= sin (α + α)

Use the Angle Sum identity:

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

= sin (α) cos (α) + cos (α) sin (α)

= sin (α) cos (α) + cos (α) sin (α)

Simplify

sin (α) cos (α) + cos (α) sin (α) : 2 sin (α) cos (α)

sin (α) cos (α) + cos (α) sin (α)

Add similar elements:

sin (α) cos (α) + cos (α) sin (α) = 2 sin (α) cos (α)

= 2 sin (α) cos (α)

= 2 sin (α) cos (α)

We showed that the two sides could take the same form

\Rightarrow True

cos (θ + π) = - cos (θ)

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

(1 + csc (x)) (1 + csc (- x)) = - cot^{2} (x)

cos (0) - sec (0) = - sin (0) tan (0)

cot^{2} (x) sin^{2} (x) csc^{2} (x) tan^{2} (x) = 1