What is the general solution for 2+3cot^2(x)-3csc(x)=5 ?

The general solution for 2+3cot^2(x)-3csc(x)=5 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin

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2+3cot^2(x)-3csc(x)=5

2 + 3 cot^{2} (x) - 3 csc (x) = 5

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

2 + 3 cot^{2} (x) - 3 csc (x) = 5

Subtract

5

from both sides

3 cot^{2} (x) - 3 csc (x) - 3 = 0

Rewrite using trig identities

- 6 - 3 csc (x) + 3 csc^{2} (x) = 0

Solve by substitution

csc (x) = 2, csc (x) = - 1

csc (x) = 2 : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

csc (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn, x = \frac{3 π}{2} + 2 πn

- 2 = - 2 + tan (θ)

cos (A) = 0.65

sin (3 x - \frac{π}{4}) = \frac{2}{2}

sin (2 θ) = \frac{- 3}{4}, \frac{3 π}{2} \leq 2 θ \leq 2 π

3 cot (x - 1 0^{\circ}) = 4

What is the general solution for 2+3cot^2(x)-3csc(x)=5 ?
The general solution for 2+3cot^2(x)-3csc(x)=5 is x= pi/6+2pin,x=(5pi)/6+2pin,x=(3pi)/2+2pin