Is cot^4(x)+cot^2(x)=cot^2(x)csc^2(x) ?

The answer to whether cot^4(x)+cot^2(x)=cot^2(x)csc^2(x) is True

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prove cot^4(x)+cot^2(x)=cot^2(x)csc^2(x)

prove

cot^{4} (x) + cot^{2} (x) = cot^{2} (x) csc^{2} (x)

True

Solution steps

cot^{4} (x) + cot^{2} (x) = cot^{2} (x) csc^{2} (x)

Manipulating left side

cot^{4} (x) + cot^{2} (x)

Factor

cot^{2} (x) + cot^{4} (x) : cot^{2} (x) (1 + cot^{2} (x))

= (1 + cot^{2} (x)) cot^{2} (x)

Rewrite using trig identities

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

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

We showed that the two sides could take the same form

\Rightarrow True

cot^{3} (x) = cot (x) (csc^{2} (x) - 1)

sin (2 a) = \frac{2 tan ( a )}{1 + tan ^{2} ( a )}

10 sec^{2} (θ) - 4 tan^{2} (θ) = 4 + 6 sec^{2} (θ)

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

sin^{2} (a) - cos^{2} (a) = 1 - 2 cos^{2} (a)

Is cot^4(x)+cot^2(x)=cot^2(x)csc^2(x) ?
The answer to whether cot^4(x)+cot^2(x)=cot^2(x)csc^2(x) is True