Is (tan(y))/(csc(y))=sec(y)-cos(y) ?

The answer to whether (tan(y))/(csc(y))=sec(y)-cos(y) is True

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prove (tan(y))/(csc(y))=sec(y)-cos(y)

prove

\frac{tan ( y )}{csc ( y )} = sec (y) - cos (y)

True

Solution steps

\frac{tan ( y )}{csc ( y )} = sec (y) - cos (y)

Manipulating left side

\frac{tan ( y )}{csc ( y )}

Express with sin, cos

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

Rewrite using trig identities

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

Manipulating right side

sec (y) - cos (y)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

cos (3 x) = cos (2 x + x)

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

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

1 - sin^{2} (θ) = cos^{2} (θ)

sin (8 x) = 2 sin (4 x) cos (4 x)

Is (tan(y))/(csc(y))=sec(y)-cos(y) ?
The answer to whether (tan(y))/(csc(y))=sec(y)-cos(y) is True