What is the general solution for (5sin(x)+6)/(sin(x))=17 ?

The general solution for (5sin(x)+6)/(sin(x))=17 is x= pi/6+2pin,x=(5pi)/6+2pin

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(5sin(x)+6)/(sin(x))=17

\frac{5 sin ( x ) + 6}{sin ( x )} = 17

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

Solution steps

\frac{5 sin ( x ) + 6}{sin ( x )} = 17

Solve by substitution

sin (x) = \frac{1}{2}

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

tan^{2} (x) sec (x) - 1 = 0

sin^{2} (x) + cos^{4} (x) = 2

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

cos (x) = 53

sin^{2} (a) = \frac{1 - cos ( a )}{2}

What is the general solution for (5sin(x)+6)/(sin(x))=17 ?
The general solution for (5sin(x)+6)/(sin(x))=17 is x= pi/6+2pin,x=(5pi)/6+2pin