What is the general solution for -4cos^2(x)+4sqrt(2)sin(x)+6=0 ?

The general solution for -4cos^2(x)+4sqrt(2)sin(x)+6=0 is x=(5pi)/4+2pin,x=(7pi)/4+2pin

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-4cos^2(x)+4sqrt(2)sin(x)+6=0

- 4 cos^{2} (x) + 42 sin (x) + 6 = 0

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

Solution steps

- 4 cos^{2} (x) + 42 sin (x) + 6 = 0

Rewrite using trig identities

2 + 4 sin^{2} (x) + 4 sin (x) 2 = 0

Solve by substitution

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

sin (x) = - \frac{2}{2} : x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

Combine all the solutions

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

sin (2 x - 1 0^{\circ}) = 0.4

\frac{1}{sin ^{2} ( x )} = 4

- 6 cos^{2} (θ) - 9 cos (θ) - 7 = 8 cos (θ)

θ, 1 + cos (θ) = 1 - sin (θ)

sin (x) = 1

What is the general solution for -4cos^2(x)+4sqrt(2)sin(x)+6=0 ?
The general solution for -4cos^2(x)+4sqrt(2)sin(x)+6=0 is x=(5pi)/4+2pin,x=(7pi)/4+2pin