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

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

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

prove

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

True

Solution steps

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

Manipulating left side

sec (x) + tan (x)

Express with sin, cos

sec (x) + tan (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

Simplify

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

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

Apply rule

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

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

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sin ( x )}{cos ( x ) cot ^{2} ( x )} = tan (x)

cos (θ) - cos (θ) sin^{2} (θ) = cos^{3} (θ)

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

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

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