Is 4cot^2(y)(sec^2(y)-1)=4 ?

The answer to whether 4cot^2(y)(sec^2(y)-1)=4 is True

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prove 4cot^2(y)(sec^2(y)-1)=4

prove

4 cot^{2} (y) (sec^{2} (y) - 1) = 4

True

Solution steps

4 cot^{2} (y) (sec^{2} (y) - 1) = 4

Manipulating left side

4 cot^{2} (y) (sec^{2} (y) - 1)

Express with sin, cos

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

Rewrite using trig identities

= 4

We showed that the two sides could take the same form

\Rightarrow True

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

sin^{2} (x) sec (x) = \frac{sin ( x )}{cot ( x )}

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

\frac{sec ^{2} ( a ) cot ( a )}{csc ^{2} ( a )} = tan (a)

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

Is 4cot^2(y)(sec^2(y)-1)=4 ?
The answer to whether 4cot^2(y)(sec^2(y)-1)=4 is True