Question 824146
find all solutions of the equation 9sec(x) csc(x)=18csc(x) in the interval [0,2pi)
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{{{9sec(x)csc(x)=18csc(x)}}}
..
{{{(9/cos(x))(1/sin(x))=(18/sin(x))}}}
..
divide both sides by 9
{{{(1/(cos(x)sin(x)))=(2/sin(x))}}}
multiply both sides by sin(x)
{{{(1/cos(x))=2}}}
cos(x)=1/2
x=π/3,5π/3 (in quadrants I and IV in which cos>0)