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

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

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

prove

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

True

Solution steps

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

Manipulating right side

csc^{4} (x) - csc^{2} (x)

Factor

- csc^{2} (x) + csc^{4} (x) : csc^{2} (x) (- 1 + csc^{2} (x))

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

Rewrite using trig identities

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

Expand

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

tan (θ) + cot (θ) = \frac{1}{sin ( θ ) \cdot cos ( θ )}

cos (θ) cot (θ) = csc (θ) - sin (θ)

1 - tanh^{2} (x) = sech^{2} (x)

sin (x) (tan (x) + cot (x)) = sec (x)

cos (π - x) = - cos (x)

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