What is the general solution for csc(x)cos^2(x)+sin^2(x)=csc(x) ?

The general solution for csc(x)cos^2(x)+sin^2(x)=csc(x) is x= pi/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

csc(x)cos^2(x)+sin^2(x)=csc(x)

csc (x) cos^{2} (x) + sin^{2} (x) = csc (x)

x = \frac{π}{2} + 2 πn

Solution steps

csc (x) cos^{2} (x) + sin^{2} (x) = csc (x)

Subtract

csc (x)

from both sides

cos^{2} (x) csc (x) + sin^{2} (x) - csc (x) = 0

Rewrite using trig identities

sin^{2} (x) - csc (x) sin^{2} (x) = 0

Factor

sin^{2} (x) - csc (x) sin^{2} (x) : - sin^{2} (x) (csc (x) - 1)

- sin^{2} (x) (csc (x) - 1) = 0

Solving each part separately

sin^{2} (x) = 0 or csc (x) - 1 = 0

sin^{2} (x) = 0 : x = 2 πn, x = π + 2 πn

csc (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = 2 πn, x = π + 2 πn, x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

2 πn, π + 2 πn

x = \frac{π}{2} + 2 πn

0.87 = 5 cos (3 x)

cos (\frac{2 π x}{3}) = \frac{1}{2}

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

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

- 1 + tan (x) = sec (x)

What is the general solution for csc(x)cos^2(x)+sin^2(x)=csc(x) ?
The general solution for csc(x)cos^2(x)+sin^2(x)=csc(x) is x= pi/2+2pin