What is the general solution for 4cos^2(x)-4sin(x)-5=0 ?

The general solution for 4cos^2(x)-4sin(x)-5=0 is 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 >

4cos^2(x)-4sin(x)-5=0

4 cos^{2} (x) - 4 sin (x) - 5 = 0

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

Solution steps

4 cos^{2} (x) - 4 sin (x) - 5 = 0

Rewrite using trig identities

- 1 - 4 sin (x) - 4 sin^{2} (x) = 0

Solve by substitution

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

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

x, tan (x^{2} + y^{2}) = 1

2 tan (x) + sec (x) = 0

2 sin (x) cos (x) - 7 cos (x) = 0

3 sin (x) = cos (x)

cos (3 x) - cos (x) = 0

What is the general solution for 4cos^2(x)-4sin(x)-5=0 ?
The general solution for 4cos^2(x)-4sin(x)-5=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin