Is csc^2(y)tan^2(y)-1=tan^2(y) ?

The answer to whether csc^2(y)tan^2(y)-1=tan^2(y) is True

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prove csc^2(y)tan^2(y)-1=tan^2(y)

prove

csc^{2} (y) tan^{2} (y) - 1 = tan^{2} (y)

True

Solution steps

csc^{2} (y) tan^{2} (y) - 1 = tan^{2} (y)

Manipulating left side

csc^{2} (y) tan^{2} (y) - 1

Express with sin, cos

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

Rewrite using trig identities

= \frac{sin ^{2} ( y )}{cos ^{2} ( y )}

Rewrite using trig identities

tan^{2} (y)

We showed that the two sides could take the same form

\Rightarrow True

cot (θ) tan (θ) = 1

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

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

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

cos (x) + sin (x) \cdot tan (x) = sec (x)

Is csc^2(y)tan^2(y)-1=tan^2(y) ?
The answer to whether csc^2(y)tan^2(y)-1=tan^2(y) is True