What is the general solution for 5cos(x)+sqrt(2)=3cos(x) ?

The general solution for 5cos(x)+sqrt(2)=3cos(x) is x=(3pi)/4+2pin,x=(5pi)/4+2pin

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5cos(x)+sqrt(2)=3cos(x)

5 cos (x) + 2 = 3 cos (x)

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Solution steps

5 cos (x) + 2 = 3 cos (x)

Solve by substitution

cos (x) = - \frac{2}{2}

cos (x) = - \frac{2}{2} : x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

Combine all the solutions

x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn

- 2 sin^{2} (θ) + 10 sin (θ) - 3 = 3 sin (θ)

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

tan (π - θ) = tan (θ)

8 cos (x) = sec^{2} (x)

5 cot (θ) - 4 = 0

What is the general solution for 5cos(x)+sqrt(2)=3cos(x) ?
The general solution for 5cos(x)+sqrt(2)=3cos(x) is x=(3pi)/4+2pin,x=(5pi)/4+2pin