What is the general solution for 11=3csc^2(x)+7 ?

The general solution for 11=3csc^2(x)+7 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin

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11=3csc^2(x)+7

11 = 3 csc^{2} (x) + 7

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Solution steps

11 = 3 csc^{2} (x) + 7

Switch sides

3 csc^{2} (x) + 7 = 11

Solve by substitution

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

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

csc (x) = - \frac{2 3}{3} : x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

Combine all the solutions

x = \frac{π}{3} + 2 πn, x = \frac{2 π}{3} + 2 πn, x = \frac{4 π}{3} + 2 πn, x = \frac{5 π}{3} + 2 πn

cos (x) tan (x) = \frac{1}{2}

4 sin^{2} (x) = 1 - 4 cos (x)

- 100 sin (10 x) = 0

2 sin (x) = csc (x) - 6, 0 \leq x < 2 π

sin (x) sec (x) - sin (x) = 0

What is the general solution for 11=3csc^2(x)+7 ?
The general solution for 11=3csc^2(x)+7 is x= pi/3+2pin,x=(2pi)/3+2pin,x=(4pi)/3+2pin,x=(5pi)/3+2pin