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

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

Popular >

prove (1+cos(θ))/(tan(θ)+sin(θ))=cot(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= \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

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

(tan (x) sec (- x)) cos (x) = sin (x) - 1

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

2 cos^{2} (x) = 0

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

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