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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

prove

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

True

Solution steps

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

tan (x) - 1 = cot (x)

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

sin (x + y) + sin (x - y) = 2 cos (x) sin (y)

cot (A) = \frac{cos ( A )}{sin ( A )}

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