What is the general solution for 2sin^2(t)-3cos(t)=3 ?

The general solution for 2sin^2(t)-3cos(t)=3 is t=pi+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin

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2sin^2(t)-3cos(t)=3

2 sin^{2} (t) - 3 cos (t) = 3

t = π + 2 πn, t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

Solution steps

2 sin^{2} (t) - 3 cos (t) = 3

Subtract

3

from both sides

2 sin^{2} (t) - 3 cos (t) - 3 = 0

Rewrite using trig identities

- 1 - 2 cos^{2} (t) - 3 cos (t) = 0

Solve by substitution

cos (t) = - 1, cos (t) = - \frac{1}{2}

cos (t) = - 1 : t = π + 2 πn

cos (t) = - \frac{1}{2} : t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

Combine all the solutions

t = π + 2 πn, t = \frac{2 π}{3} + 2 πn, t = \frac{4 π}{3} + 2 πn

cos (x) = \frac{3}{2}, 0 \leq x \leq 2 π

csc^{2} (x) + 4 csc (x) + 4 = 0

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

2 sin (2 x) cos (x) + sin (x) = 0

4 cos (x) + 1 = 3

What is the general solution for 2sin^2(t)-3cos(t)=3 ?
The general solution for 2sin^2(t)-3cos(t)=3 is t=pi+2pin,t=(2pi)/3+2pin,t=(4pi)/3+2pin