Question

Solve csc(2x)−4=0csc(2x)-4=0 for the four smallest positive solutions

Answer #1

Solution:-

Cosec(2x) -4=0

Or cosec(2x)=4 .........1

Since cosec(2x)=1/sin(2x)

Putting this in equation 1,we get

1/sin(2x)=4

1/4=sin(2x)

Or sin(2x)=1/4

Sin2x=Sin(0.25268)

Or 2x=0.25268 radian

Sincce, Sin(2x) is positive in 1st and 2nd quadrant

So, four positive values of 2x will be

2x= 0.25268 , (π-0.25268} , (2π+0.25268), (3π-0.25268)

Or 2x=0.25268 , 2.888 , 6.03 , 9.172

Or x= 0.12634 , 1.444 , 3.015 , 4.586

Note:-These values are in radian.To convert them in degree multiply each value by (180°/π).

Hence the required answers (in radian)are

x=0.12634 , 1.444, 3.015 , 4.586

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