What is the general solution for 6cos^2(x)-5sin(x)+5=0 ?

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

11 - 5 sin (x) - 6 sin^{2} (x) = 0

Solve by substitution

sin (x) = - \frac{11}{6}, sin (x) = 1

sin (x) = - \frac{11}{6} :

No Solution

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

1 + cos^{2} (a) = 3 sin (x) cos (x)

3 cos (x) + sin (x) = cos (x) - 2 sin (x)

2 cos (x) = cos^{2} (x)

tan^{2} (x) - sin (x) = tan^{2} (x) sin^{2} (x)

3 cos (a) - 1 = 0

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