Is tan(a)+sec(a)=(1+sin(a))/(cos(a)) ?

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

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prove tan(a)+sec(a)=(1+sin(a))/(cos(a))

prove

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

True

Solution steps

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

Manipulating left side

tan (a) + sec (a)

Express with sin, cos

sec (a) + tan (a)

Use the basic trigonometric identity:

sec (x) = \frac{1}{cos ( x )}

= \frac{1}{cos ( a )} + tan (a)

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

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

Simplify

\frac{1}{cos ( a )} + \frac{sin ( a )}{cos ( a )} : \frac{1 + sin ( a )}{cos ( a )}

\frac{1}{cos ( a )} + \frac{sin ( a )}{cos ( a )}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

\frac{sin ( 3 a )}{sin ( a )} = 2 cos (2 a) + 1

\frac{1}{sin ( x ) cos ( x )} = \frac{sec ( x )}{sin ( x )}

sin (2 x) + cos (2 x) = 1 + 2 sin (x) cos (x)

\frac{cot ^{2} ( x ) + 1}{cot ^{2} ( x ) - 1} = sec (2 x)

- (3) \frac{sin ^{2} ( 2 z )}{2} = \frac{3 cos ( 4 z )}{4}

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