Is (cot(x))(sec(x))(sin(x))=1 ?

The answer to whether (cot(x))(sec(x))(sin(x))=1 is True

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

prove (cot(x))(sec(x))(sin(x))=1

prove

(cot (x)) (sec (x)) (sin (x)) = 1

True

Solution steps

cot (x) sec (x) sin (x) = 1

Manipulating left side

cot (x) sec (x) sin (x)

Express with sin, cos

cot (x) sec (x) sin (x)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (x)

= \frac{1 \cdot sin ( x )}{sin ( x )}

Cancel the common factor:

sin (x)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ^{2} ( x ) - 4}{cos ( x ) - 2} = cos (x) + 2

sin^{2} (a) tan^{2} (a) = tan^{2} (a) - sin^{2} (a)

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

tan (θ) (sin (θ) + cot (θ) cos (θ)) = sec (θ)

sin (x + y) = sin (x) + sin (y)

Is (cot(x))(sec(x))(sin(x))=1 ?
The answer to whether (cot(x))(sec(x))(sin(x))=1 is True