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

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

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sec(x)(2cos(x)-sqrt(2))=0

sec (x) (2 cos (x) - 2) = 0

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

Solution steps

sec (x) (2 cos (x) - 2) = 0

Solving each part separately

sec (x) = 0 or 2 cos (x) - 2 = 0

sec (x) = 0 :

No Solution

2 cos (x) - 2 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

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

2 cos (θ) - 2 = 0

sin (x) - 2 = 0

x, sin^{4} (x) = \frac{cos ^{2} ( x )}{2}

tan^{2} (x) + 5 tan (x) - 1 = 0

csc (θ) + 1 = 0

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