en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-2sin^2(x)+2cos(x)+2cos^2(x)=0

Solution

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

Solution

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

+1

Solution steps

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

Rewrite using trig identities

- 2 + 2 cos (x) + 4 cos^{2} (x) = 0

Solve by substitution

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

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn, x = π + 2 πn

Popular Examples

1+2sin^2(t)=-5cos(t)

1 + 2 sin^{2} (t) = - 5 cos (t)

2sin(2x)-3-6/(sin(2x)-1)=0

2 sin (2 x) - 3 - \frac{6}{sin ( 2 x ) - 1} = 0

3sin^2(x)+11sin(x)+10=0

3 sin^{2} (x) + 11 sin (x) + 10 = 0

cos(x)(cos(x)+5)=2sin^2(x)

cos (x) (cos (x) + 5) = 2 sin^{2} (x)

tan^2(x)+3tan(x)-10=0

tan^{2} (x) + 3 tan (x) - 10 = 0

Frequently Asked Questions (FAQ)

What is the general solution for -2sin^2(x)+2cos(x)+2cos^2(x)=0 ?
The general solution for -2sin^2(x)+2cos(x)+2cos^2(x)=0 is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin