What is the general solution for 6cos^2(x)-7sin(x)-1=0 ?

The general solution for 6cos^2(x)-7sin(x)-1=0 is x= pi/6+2pin,x=(5pi)/6+2pin

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6cos^2(x)-7sin(x)-1=0

6 cos^{2} (x) - 7 sin (x) - 1 = 0

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

Solution steps

6 cos^{2} (x) - 7 sin (x) - 1 = 0

Rewrite using trig identities

5 - 6 sin^{2} (x) - 7 sin (x) = 0

Solve by substitution

sin (x) = - \frac{5}{3}, sin (x) = \frac{1}{2}

sin (x) = - \frac{5}{3} :

No Solution

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

2 sin^{2} (θ) + 3 sin (θ) + 1 = 0

1 = sin (x)

sin (2 x) = - cos (x)

cos (2 θ) = cos (θ)

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

What is the general solution for 6cos^2(x)-7sin(x)-1=0 ?
The general solution for 6cos^2(x)-7sin(x)-1=0 is x= pi/6+2pin,x=(5pi)/6+2pin