Is (1-cos(2θ)+sin(2θ))/(1+cos(2θ)+sin(2θ))=tan(θ) ?

The answer to whether (1-cos(2θ)+sin(2θ))/(1+cos(2θ)+sin(2θ))=tan(θ) is True

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prove (1-cos(2θ)+sin(2θ))/(1+cos(2θ)+sin(2θ))=tan(θ)

prove

\frac{1 - cos ( 2 θ ) + sin ( 2 θ )}{1 + cos ( 2 θ ) + sin ( 2 θ )} = tan (θ)

True

Solution steps

\frac{1 - cos ( 2 θ ) + sin ( 2 θ )}{1 + cos ( 2 θ ) + sin ( 2 θ )} = tan (θ)

Manipulating left side

\frac{1 - cos ( 2 θ ) + sin ( 2 θ )}{1 + cos ( 2 θ ) + sin ( 2 θ )}

Rewrite using trig identities

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{cos ( θ )}{cos ( θ ) - 1} = \frac{1}{1 - sec ( θ )}

cos (- \frac{π}{4} - 5 t) = cos (5 t + \frac{π}{4})

tan (\frac{π}{4} - θ) = \frac{1 - tan ( θ )}{1 + tan ( θ )}

\frac{sin ( θ )}{cot ( θ ) + csc ( θ )} = 1 - cos (θ)

Is (1-cos(2θ)+sin(2θ))/(1+cos(2θ)+sin(2θ))=tan(θ) ?
The answer to whether (1-cos(2θ)+sin(2θ))/(1+cos(2θ)+sin(2θ))=tan(θ) is True