Is ((csc^2(x)))/(cot(x))=csc(x)sec(x) ?

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

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prove ((csc^2(x)))/(cot(x))=csc(x)sec(x)

prove

\frac{( csc ^{2} ( x ) )}{cot ( x )} = csc (x) sec (x)

True

Solution steps

\frac{csc ^{2} ( x )}{cot ( x )} = csc (x) sec (x)

Manipulating left side

\frac{csc ^{2} ( x )}{cot ( x )}

Express with sin, cos

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

Rewrite using trig identities

sec (x) csc (x)

= csc (x) sec (x)

We showed that the two sides could take the same form

\Rightarrow True

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

sin (x) cos (x) + sin (3 x) sec (x) = tan (x)

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

(sec (α)) (sec (α)) = tan (α)

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

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