What is the general solution for solvefor x,4cos^2(x)=5-4sin(x) ?

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

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solvefor x,4cos^2(x)=5-4sin(x)

solve for

x, 4 cos^{2} (x) = 5 - 4 sin (x)

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

4 cos^{2} (x) = 5 - 4 sin (x)

Subtract

5 - 4 sin (x)

from both sides

4 cos^{2} (x) - 5 + 4 sin (x) = 0

Rewrite using trig identities

- 1 + 4 sin (x) - 4 sin^{2} (x) = 0

Solve by substitution

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

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

cos (x) = \frac{2}{3}, - \frac{5 π}{2} < x < 2 π

\frac{3 sin ( x ) - cos ( x )}{sin ( x ) + cos ( x )} = 4

\frac{1}{e ^{s i n (x)}} = 1

∣ cos (x) ∣ = \frac{3}{2}

tan (θ) = \frac{- 1}{3}, 0^{\circ} \leq θ \leq 36 0^{\circ}

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