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

3 tan^{2} (x) - 10 tan (x) + 7 = 0

cos (x) = - \frac{3}{3}

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

θ, 2 cos (θ) + 1 = 0

- 4 + tan (θ) = \frac{- 12 - 3}{3}

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