What is the general solution for cos(2x)-3cos(x)-4=0 ?

The general solution for cos(2x)-3cos(x)-4=0 is x=pi+2pin

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cos(2x)-3cos(x)-4=0

cos (2 x) - 3 cos (x) - 4 = 0

x = π + 2 πn

Solution steps

cos (2 x) - 3 cos (x) - 4 = 0

Rewrite using trig identities

- 5 + 2 cos^{2} (x) - 3 cos (x) = 0

Solve by substitution

cos (x) = \frac{5}{2}, cos (x) = - 1

cos (x) = \frac{5}{2} :

No Solution

cos (x) = - 1 : x = π + 2 πn

Combine all the solutions

x = π + 2 πn

3 - 5 cos (θ) = 0

tan (x) = \frac{48}{50}

\frac{sin ( 5 4 ^{\circ} )}{7} = \frac{sin ( x )}{10}

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

5 sin (3 x) - 11 = 3 sin (3 x) - 12

What is the general solution for cos(2x)-3cos(x)-4=0 ?
The general solution for cos(2x)-3cos(x)-4=0 is x=pi+2pin