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

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

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

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

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

Solution steps

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

Solving each part separately

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

sin (x) = 0 : x = 2 πn, x = π + 2 πn

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

Combine all the solutions

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

sin (θ) = \frac{- 2}{2}

cos (θ) csc (θ) = - 2 cos (θ)

csc^{2} (x) - 4 cot (x) = - 2

sin (2 x - \frac{π}{3}) = \frac{3}{2}

- sin^{3} (t) + sin (2 t) cos (t) = 0

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