What is the general solution for sin^2(x)-cos^2(x)-sin(x)=0 ?

The general solution for sin^2(x)-cos^2(x)-sin(x)=0 is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

10 tan (x) sin (x) = sin (x)

cos (2 x) = 2 sin (x) cos (x)

sin (θ) = \frac{5}{6}

3 tan^{2} (x) = 3 tan (x)

2 sec (x) - 4 cos (x) = 0

What is the general solution for sin^2(x)-cos^2(x)-sin(x)=0 ?
The general solution for sin^2(x)-cos^2(x)-sin(x)=0 is x= pi/2+2pin,x=(7pi)/6+2pin,x=(11pi)/6+2pin