What is the general solution for 2cos(x/5)-sqrt(2)=0 ?

The general solution for 2cos(x/5)-sqrt(2)=0 is x=(5pi)/4+10pin,x=(35pi)/4+10pin

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2cos(x/5)-sqrt(2)=0

2 cos (\frac{x}{5}) - 2 = 0

x = \frac{5 π}{4} + 10 πn, x = \frac{35 π}{4} + 10 πn

Solution steps

2 cos (\frac{x}{5}) - 2 = 0

Move

2

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{x}{5} = \frac{π}{4} + 2 πn, \frac{x}{5} = \frac{7 π}{4} + 2 πn

Solve

\frac{x}{5} = \frac{π}{4} + 2 πn : x = \frac{5 π}{4} + 10 πn

Solve

\frac{x}{5} = \frac{7 π}{4} + 2 πn : x = \frac{35 π}{4} + 10 πn

x = \frac{5 π}{4} + 10 πn, x = \frac{35 π}{4} + 10 πn

2 sin^{2} (x) + 3 = 7 sin (x)

4 sin (x) = cos (x)

25 sin^{2} (θ) - 1 = 0

2 cos (x) sin (x) + 9 sin (x) = 0

1 - sin (x) = 0

What is the general solution for 2cos(x/5)-sqrt(2)=0 ?
The general solution for 2cos(x/5)-sqrt(2)=0 is x=(5pi)/4+10pin,x=(35pi)/4+10pin