Is 1/(1-sin(t))=sec^2(t)+sec(t)tan(t) ?

The answer to whether 1/(1-sin(t))=sec^2(t)+sec(t)tan(t) is True

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prove 1/(1-sin(t))=sec^2(t)+sec(t)tan(t)

prove

\frac{1}{1 - sin ( t )} = sec^{2} (t) + sec (t) tan (t)

True

Solution steps

\frac{1}{1 - sin ( t )} = sec^{2} (t) + sec (t) tan (t)

Manipulating right side

sec^{2} (t) + sec (t) tan (t)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{1 - sin ( t )}

We showed that the two sides could take the same form

\Rightarrow True

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

sec^{2} (x) cos (x) - sec (x) = 0

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

sec (z) cot (z) sin (z) = 1

cos (θ) = \frac{2}{3}

Is 1/(1-sin(t))=sec^2(t)+sec(t)tan(t) ?
The answer to whether 1/(1-sin(t))=sec^2(t)+sec(t)tan(t) is True