What is the general solution for 2cos^2(x)-8cos(x)=2sin^2(x)-5 ?

The general solution for 2cos^2(x)-8cos(x)=2sin^2(x)-5 is x= pi/3+2pin,x=(5pi)/3+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2cos^2(x)-8cos(x)=2sin^2(x)-5

2 cos^{2} (x) - 8 cos (x) = 2 sin^{2} (x) - 5

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

Solution steps

2 cos^{2} (x) - 8 cos (x) = 2 sin^{2} (x) - 5

Subtract

2 sin^{2} (x) - 5

from both sides

2 cos^{2} (x) - 8 cos (x) - 2 sin^{2} (x) + 5 = 0

Rewrite using trig identities

3 + 4 cos^{2} (x) - 8 cos (x) = 0

Solve by substitution

cos (x) = \frac{3}{2}, cos (x) = \frac{1}{2}

cos (x) = \frac{3}{2} :

No Solution

cos (x) = \frac{1}{2} : x = \frac{π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

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

2 cos^{2} (a) tan (a) = tan (a)

sin^{2} (x) + 5 sin (x) + 5 = 0

cos (x) = - 0.814

3 cos^{2} (x) - 8 cos (x) + 4 = sin^{2} (x)

cos (x - 4 5^{\circ}) = \frac{- 1}{2}

What is the general solution for 2cos^2(x)-8cos(x)=2sin^2(x)-5 ?
The general solution for 2cos^2(x)-8cos(x)=2sin^2(x)-5 is x= pi/3+2pin,x=(5pi)/3+2pin