What is the general solution for 2cos(1/2 x)-sqrt(2)=0 ?

The general solution for 2cos(1/2 x)-sqrt(2)=0 is x= pi/2+4pin,x=(7pi)/2+4pin

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2cos(1/2 x)-sqrt(2)=0

2 cos (\frac{1}{2} x) - 2 = 0

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

Solution steps

2 cos (\frac{1}{2} x) - 2 = 0

Move

2

to the right side

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

Divide both sides by

2

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

General solutions for

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

\frac{1}{2} x = \frac{π}{4} + 2 πn, \frac{1}{2} x = \frac{7 π}{4} + 2 πn

Solve

\frac{1}{2} x = \frac{π}{4} + 2 πn : x = \frac{π}{2} + 4 πn

Solve

\frac{1}{2} x = \frac{7 π}{4} + 2 πn : x = \frac{7 π}{2} + 4 πn

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

cos (\frac{π}{x}) = 0

tan^{2} (θ) - 4 sec (θ) = - 5

tan (θ) = \frac{5}{6}

sin (3 x) cos (2 x) + cos (3 x) sin (2 x) = 1

tan^{2} (θ) + 4 tan (θ) = 3

What is the general solution for 2cos(1/2 x)-sqrt(2)=0 ?
The general solution for 2cos(1/2 x)-sqrt(2)=0 is x= pi/2+4pin,x=(7pi)/2+4pin