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

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

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prove sin^2(x)(csc^2(x)-1)=cos^2(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

= 1 - sin^{2} (x)

Rewrite using trig identities

= cos^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

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

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

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

cos (3 α) = 4 cos^{3} (α) - 3 cos (α)

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

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