What is the general solution for 8sin(x)=4cos^2(x)-7 ?

The general solution for 8sin(x)=4cos^2(x)-7 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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8sin(x)=4cos^2(x)-7

8 sin (x) = 4 cos^{2} (x) - 7

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

Solution steps

8 sin (x) = 4 cos^{2} (x) - 7

Subtract

4 cos^{2} (x) - 7

from both sides

8 sin (x) - 4 cos^{2} (x) + 7 = 0

Rewrite using trig identities

3 + 4 sin^{2} (x) + 8 sin (x) = 0

Solve by substitution

sin (x) = - \frac{1}{2}, sin (x) = - \frac{3}{2}

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = - \frac{3}{2} :

No Solution

Combine all the solutions

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

cos (x) - 1 = 0, 0 \leq x \leq 2 π

sin (x) = \frac{4.8}{5.5}

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

2 csc (2 x) + 2 = 0

x, cos (x) = - sin (x)

What is the general solution for 8sin(x)=4cos^2(x)-7 ?
The general solution for 8sin(x)=4cos^2(x)-7 is x=(7pi)/6+2pin,x=(11pi)/6+2pin