Is cot(θ)*sec(θ)*sin(θ)=1 ?

The answer to whether cot(θ)*sec(θ)*sin(θ)=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(θ)sec(θ)sin(θ)=1

prove

cot (θ) \cdot sec (θ) \cdot sin (θ) = 1

True

Solution steps

cot (θ) sec (θ) sin (θ) = 1

Manipulating left side

cot (θ) sec (θ) sin (θ)

Express with sin, cos

cot (θ) sec (θ) sin (θ)

Use the basic trigonometric identity:

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

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

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

cos (θ)

= \frac{1 \cdot sin ( θ )}{sin ( θ )}

Cancel the common factor:

sin (θ)

= 1

= 1

= 1

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sec ^{2} ( t )} = (1 + sin (t)) (1 - sin (t))

cos (2 0^{\circ}) = cos (θ) cos (θ) - sin (θ) sin (θ)

cos (θ) = \frac{4}{5}

\frac{2 sin ( 2 θ ) cos ( θ )}{2 sin ( 2 θ )} = cos (θ)

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

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