Is csc(2θ)+cot(2θ)=cot(θ) ?

The answer to whether csc(2θ)+cot(2θ)=cot(θ) is True

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prove csc(2θ)+cot(2θ)=cot(θ)

prove

csc (2 θ) + cot (2 θ) = cot (θ)

True

Solution steps

csc (2 θ) + cot (2 θ) = cot (θ)

Manipulating left side

csc (2 θ) + cot (2 θ)

Express with sin, cos

= \frac{1 + cos ( 2 θ )}{sin ( 2 θ )}

Rewrite using trig identities

= \frac{cos ( θ )}{sin ( θ )}

Use the basic trigonometric identity:

\frac{cos ( x )}{sin ( x )} = cot (x)

= cot (θ)

We showed that the two sides could take the same form

\Rightarrow True

- tan (x) cos (x) = sin (- x)

sin (x - \frac{3 π}{2}) = cos (x)

cos (x + 2 π) = cos (x)

sin^{2} (x) = \frac{( 1 - cos ( 2 x ) )}{2}

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

Is csc(2θ)+cot(2θ)=cot(θ) ?
The answer to whether csc(2θ)+cot(2θ)=cot(θ) is True