Is 2sin(θ)cos(θ)=sin(2θ) ?

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

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prove 2sin(θ)cos(θ)=sin(2θ)

prove

2 sin (θ) cos (θ) = sin (2 θ)

True

Solution steps

2 sin (θ) cos (θ) = sin (2 θ)

Manipulating right side

sin (2 θ)

Rewrite using trig identities

= sin (θ) cos (θ) + cos (θ) sin (θ)

Simplify

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

= 2 sin (θ) cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

tan^{4} (x) + tan^{2} (x) + 1 = sec^{4} (x)

tan^{3} (x) - cot^{3} (x) = tan^{2} (x) sin^{2} (x)

csc^{2} (θ) = cot^{2} (θ) + 1

\frac{1 + tan ^{2} ( x )}{tan ( x )} = sec (x) csc (x)

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