Is prove-tan(y)+sec(y)=(cos(y))/(1+sin(y)) ?

The answer to whether prove-tan(y)+sec(y)=(cos(y))/(1+sin(y)) is True

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prove-tan(y)+sec(y)=(cos(y))/(1+sin(y))

prove

- tan (y) + sec (y) = \frac{cos ( y )}{1 + sin ( y )}

True

Solution steps

- tan (y) + sec (y) = \frac{cos ( y )}{1 + sin ( y )}

Manipulating left side

- tan (y) + sec (y)

Express with sin, cos

= \frac{1 - sin ( y )}{cos ( y )}

Rewrite using trig identities

= \frac{cos ( y )}{1 + sin ( y )}

We showed that the two sides could take the same form

\Rightarrow True

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

sin (2 z) = 2 sin (z) cos (z)

csc^{2} (a) sec^{2} (a) = sec^{2} (a) + csc^{2} (a)

(sin^{2} (x)) (1 + cot^{2} (x)) = 1

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

Is prove-tan(y)+sec(y)=(cos(y))/(1+sin(y)) ?
The answer to whether prove-tan(y)+sec(y)=(cos(y))/(1+sin(y)) is True