What is the general solution for sin^2(x)=2sin^2(x/2) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin^2(x)=2sin^2(x/2)

sin^{2} (x) = 2 sin^{2} (\frac{x}{2})

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

Solution steps

sin^{2} (x) = 2 sin^{2} (\frac{x}{2})

Subtract

2 sin^{2} (\frac{x}{2})

from both sides

sin^{2} (x) - 2 sin^{2} (\frac{x}{2}) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = 1

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 1 : x = 2 πn

Combine all the solutions

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

5 sin (x) = cos (x) - 4

tan (x) - 3 = 0

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

- 21 tan (x) + 33 = - 3 (3 + tan (x))

tan (y) = - 1

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