What is the general solution for 2cos(x)+2=4sin^2(x) ?

The general solution for 2cos(x)+2=4sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos(x)+2=4sin^2(x)

2 cos (x) + 2 = 4 sin^{2} (x)

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

Solution steps

2 cos (x) + 2 = 4 sin^{2} (x)

Subtract

4 sin^{2} (x)

from both sides

2 cos (x) + 2 - 4 sin^{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

tan (x) + cot (x) = 5

5 sin^{2} (θ) + 12 sin (θ) + 7 = 0

3 sin (x) + 2 sin^{2} (x) = - 1

(tan (x) + 3) (2 sin (x) - 2) = 0

3 cos^{2} (x) - 2 cos (x) - 2 = 0, 0 \leq x < 2 π

What is the general solution for 2cos(x)+2=4sin^2(x) ?
The general solution for 2cos(x)+2=4sin^2(x) is x= pi/3+2pin,x=(5pi)/3+2pin,x=pi+2pin