Is (cos(θ)+cot(θ))/(csc(θ)+1)=cos(θ) ?

The answer to whether (cos(θ)+cot(θ))/(csc(θ)+1)=cos(θ) is True

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prove (cos(θ)+cot(θ))/(csc(θ)+1)=cos(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{csc ^{2} ( θ ) - 2}{csc ^{2} ( θ )} = cos (2 θ)

cos^{4} (w) + 1 - sin^{4} (w) = 2 cos^{2} (w)

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

cos (b) + sin (b) tan (b) = sec (b)

2 sin (2 θ) (1 - 2 sin^{2} (θ)) = sin (4 θ)

Is (cos(θ)+cot(θ))/(csc(θ)+1)=cos(θ) ?
The answer to whether (cos(θ)+cot(θ))/(csc(θ)+1)=cos(θ) is True