What is the general solution for sin(x)cot(x)csc(x)=sqrt(2) ?

The general solution for sin(x)cot(x)csc(x)=sqrt(2) is x=0.61547…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)cot(x)csc(x)=sqrt(2)

sin (x) cot (x) csc (x) = 2

x = 0.61547 \dots + πn

Degrees

x = 35.26438 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) cot (x) csc (x) = 2

Rewrite using trig identities

sin (x) cot (x) csc (x)

csc (x) sin (x) = 1

csc (x) sin (x)

Express with sin, cos

csc (x) sin (x)

Use the basic trigonometric identity:

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

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

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

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

Multiply fractions:

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

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

Cancel the common factor:

sin (x)

= 1

= 1

= cot (x) \cdot 1

cot (x) \cdot 1 = 2

Multiply:

cot (x) \cdot 1 = cot (x)

cot (x) = 2

Apply trig inverse properties

cot (x) = 2

General solutions for

cot (x) = 2

cot (x) = a \Rightarrow x = arccot (a) + πn

x = arccot (2) + πn

x = arccot (2) + πn

Show solutions in decimal form

x = 0.61547 \dots + πn

cos (2 x) + 4 cos (x) = - 3

1 = 2 cos (2 x)

cos (\frac{π}{6}) = sin (x)

cos (θ) = - \frac{9}{10}

arctan (x) = \frac{1}{2}

What is the general solution for sin(x)cot(x)csc(x)=sqrt(2) ?
The general solution for sin(x)cot(x)csc(x)=sqrt(2) is x=0.61547…+pin