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

The answer to whether tan(x)(csc^{(2)}(x)-1)=cot(x) is True

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

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= cot (x)

We showed that the two sides could take the same form

\Rightarrow True

sin^{4} (θ) - cos^{4} (θ) = 2 sin (θ) - 1

tan (x) - 3 = 0

\frac{sin ^{4} ( x ) - 1}{cos ^{2} ( x )} = cos^{2} (x) - 2

csc (x) tan (x) = \frac{1}{cos ( x )}

tan^{2} (A) - sin^{2} (A) = tan^{2} (A) sin^{2} (A)

Is tan(x)(csc^{(2)}(x)-1)=cot(x) ?
The answer to whether tan(x)(csc^{(2)}(x)-1)=cot(x) is True