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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

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

4 - 5 cos (x) = 4 + 3 sin (x)

\frac{tan ( θ ) cos ( θ )}{csc ( θ )} = sin (θ)

sin (θ) = \frac{44}{12}

cos (A) = \frac{2 ^{2} + 2.2 4 ^{2} - 2.2 4 ^{2}}{2 ( 2 ) ( 2.24 )}

cos (θ) = - \frac{3}{5}, θ, 3

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