Is 1/(-6csc^2(6x-1))=-(sin^2(6x-1))/6 ?

The answer to whether 1/(-6csc^2(6x-1))=-(sin^2(6x-1))/6 is True

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prove 1/(-6csc^2(6x-1))=-(sin^2(6x-1))/6

prove

\frac{1}{- 6 csc ^{2} ( 6 x - 1 )} = - \frac{sin ^{2} ( 6 x - 1 )}{6}

True

Solution steps

\frac{1}{- 6 csc ^{2} ( 6 x - 1 )} = - \frac{sin ^{2} ( 6 x - 1 )}{6}

Manipulating left side

\frac{1}{- 6 csc ^{2} ( 6 x - 1 )}

Express with sin, cos

= - \frac{sin ^{2} ( - 1 + 6 x )}{6}

= - \frac{sin ^{2} ( 6 x - 1 )}{6}

We showed that the two sides could take the same form

\Rightarrow True

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

csc (2 x) = \frac{- 2 3}{3}

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

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

(csc (θ)) (sec (θ)) - cot (θ) = tan (θ)

Is 1/(-6csc^2(6x-1))=-(sin^2(6x-1))/6 ?
The answer to whether 1/(-6csc^2(6x-1))=-(sin^2(6x-1))/6 is True