What is the general solution for 10+5cos(2x)=15cos(x) ?

The general solution for 10+5cos(2x)=15cos(x) is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin

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10+5cos(2x)=15cos(x)

10 + 5 cos (2 x) = 15 cos (x)

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

Solution steps

10 + 5 cos (2 x) = 15 cos (x)

Subtract

15 cos (x)

from both sides

10 + 5 cos (2 x) - 15 cos (x) = 0

Rewrite using trig identities

5 + 10 cos^{2} (x) - 15 cos (x) = 0

Solve by substitution

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

cos (x) = 1 : x = 2 πn

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

Combine all the solutions

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

y, x = cos (2 y)

tan (x) = \frac{a}{b}

- 1 = cot (θ)

6 sin^{2} (A) - 5 sin (A) + 1 = 0

x, arcsin (3 x - 4 y) = \frac{π}{2}

What is the general solution for 10+5cos(2x)=15cos(x) ?
The general solution for 10+5cos(2x)=15cos(x) is x=2pin,x= pi/3+2pin,x=(5pi)/3+2pin