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=(7pi)/6+2pin,x=(11pi)/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{7 π}{6} + 2 πn, x = \frac{11 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{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

t, y = cos (2 t)

cos (3 x) = \frac{1}{5}

cos^{2} (x) - 5 cos (x) + 6 = 0

cot^{2} (\frac{x}{2}) = 3, 0, 0 \leq x \leq 360

2 sin^{2} (x) + 5 sin (x) - 3 = 0, 0 \leq x \leq 2 π

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=(7pi)/6+2pin,x=(11pi)/6+2pin