Is (cos(θ)sec(θ))/(cot(θ))=tan(θ) ?

The answer to whether (cos(θ)sec(θ))/(cot(θ))=tan(θ) is True

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prove (cos(θ)sec(θ))/(cot(θ))=tan(θ)

prove

\frac{cos ( θ ) sec ( θ )}{cot ( θ )} = tan (θ)

True

Solution steps

\frac{cos ( θ ) sec ( θ )}{cot ( θ )} = tan (θ)

Manipulating left side

\frac{cos ( θ ) sec ( θ )}{cot ( θ )}

Express with sin, cos

= \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

csc^{2} (u) - cos (u) sec (u) = cot^{2} (u)

\frac{cos ^{2} ( x )}{sin ( x )} + sin (x) = csc (x)

cos^{2} (x) tan^{2} (x) = 1 - cos^{2} (x)

- csc^{2} (x) cos^{2} (x) = 1 - csc^{2} (x)

sec (θ) = sin (θ) (tan (θ) + cot (θ))

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