Is sin(2θ)=2cos(θ)*sin(θ) ?

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

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prove sin(2θ)=2cos(θ)*sin(θ)

prove

sin (2 θ) = 2 cos (θ) \cdot sin (θ)

True

Solution steps

sin (2 θ) = 2 cos (θ) sin (θ)

Manipulating left side

sin (2 θ)

Rewrite using trig identities

sin (2 θ)

Rewrite as

= sin (θ + θ)

Use the Angle Sum identity:

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

= sin (θ) cos (θ) + cos (θ) sin (θ)

= sin (θ) cos (θ) + cos (θ) sin (θ)

Simplify

sin (θ) cos (θ) + cos (θ) sin (θ) : 2 sin (θ) cos (θ)

sin (θ) cos (θ) + cos (θ) sin (θ)

Add similar elements:

sin (θ) cos (θ) + cos (θ) sin (θ) = 2 sin (θ) cos (θ)

= 2 sin (θ) cos (θ)

= 2 sin (θ) cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 + cos ( a )}{sin ( a )} = cot (\frac{a}{2})

csc (θ) sin (θ) = - \frac{8}{43}

csc (θ) sin (θ) - sin^{2} (θ) = cos^{2} (θ)

sin (\frac{π}{2} + x) = - cos (x)

tan^{2} (x) - sec (x) = 1

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