Is (tan(x))/(sin(x))=sec(x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (tan(x))/(sin(x))=sec(x)

prove

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

True

Solution steps

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

Manipulating left side

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

Express with sin, cos

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

Use the basic trigonometric identity:

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

= \frac{\frac{s i n ( x )}{c o s ( x )}}{sin ( x )}

Simplify

\frac{\frac{s i n ( x )}{c o s ( x )}}{sin ( x )} : \frac{1}{cos ( x )}

\frac{\frac{s i n ( x )}{c o s ( x )}}{sin ( x )}

Apply the fraction rule:

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

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

Cancel the common factor:

sin (x)

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

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

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

Rewrite using trig identities

Use the basic trigonometric identity:

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

\frac{1}{\frac{1}{s e c ( x )}}

Simplify

\frac{1}{\frac{1}{s e c ( x )}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Apply rule

\frac{a}{1} = a

= sec (x)

sec (x)

sec (x)

We showed that the two sides could take the same form

\Rightarrow True

(1 - sin^{2} (θ)) sec^{2} (θ) = 1

(1 + sin (a)) (1 - sin (a)) = cos^{2} (a)

sin^{3} (θ) = \frac{3}{4} sin (θ) - \frac{1}{4} sin (3 θ)

tan^{2} (θ) + 1 = sec^{2} (θ)

sin (x) + sin (3 x) = 4 sin (x) cos^{2} (x)

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