Is cot(x)sec(x)csc^2(x)-cot^3(x)sec(x)=csc(x) ?

The answer to whether cot(x)sec(x)csc^2(x)-cot^3(x)sec(x)=csc(x) is True

Popular >

prove cot(x)sec(x)csc^2(x)-cot^3(x)sec(x)=csc(x)

prove

cot (x) sec (x) csc^{2} (x) - cot^{3} (x) sec (x) = csc (x)

True

Solution steps

cot (x) sec (x) csc^{2} (x) - cot^{3} (x) sec (x) = csc (x)

Manipulating left side

cot (x) sec (x) csc^{2} (x) - cot^{3} (x) sec (x)

Express with sin, cos

= \frac{1 - cos ^{2} ( x )}{sin ^{3} ( x )}

Rewrite using trig identities

= \frac{1}{sin ( x )}

Rewrite using trig identities

csc (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) + sec (x) = \frac{1}{sin ( x ) + cos ( x )}

cos (x) \cdot cot (x) + sin (x) = csc (x)

csc (t) - sin (t) = cot (t) cos (t)

\frac{sec ( x ) + 1}{sec ( x )} = 1 + cos (x)

\frac{cos ( A )}{1 + sin ( A )} + tan (A) = sec (A)

Is cot(x)sec(x)csc^2(x)-cot^3(x)sec(x)=csc(x) ?
The answer to whether cot(x)sec(x)csc^2(x)-cot^3(x)sec(x)=csc(x) is True