Is cot(x)sec^2(x)-cot(x)=tan(x) ?

The answer to whether cot(x)sec^2(x)-cot(x)=tan(x) is True

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prove cot(x)sec^2(x)-cot(x)=tan(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

\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)

csc^{2} (x) cos^{2} (x) = cot^{2} (x)

Is cot(x)sec^2(x)-cot(x)=tan(x) ?
The answer to whether cot(x)sec^2(x)-cot(x)=tan(x) is True