What is the general solution for 2cos^2(x)=3-3sin(x) ?

The general solution for 2cos^2(x)=3-3sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos^2(x)=3-3sin(x)

2 cos^{2} (x) = 3 - 3 sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

2 cos^{2} (x) = 3 - 3 sin (x)

Subtract

3 - 3 sin (x)

from both sides

2 cos^{2} (x) - 3 + 3 sin (x) = 0

Rewrite using trig identities

- 1 - 2 sin^{2} (x) + 3 sin (x) = 0

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = 1

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

sec (3 x) - 4 = 0

6 sin^{2} (θ) + 5 sin (θ) = - 2 sin (θ) - 1

t, x = 5 cos (t)

tan (θ) = \frac{π}{2}

49 sin (2 β) = 25, tan (β) < 0

What is the general solution for 2cos^2(x)=3-3sin(x) ?
The general solution for 2cos^2(x)=3-3sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin,x= pi/2+2pin