Question

3x is equal to cosec a and 3 /x is equal to CotA find the value of 3 (x square - 1/ x square)

Answer 1

Since,3x=cosec a
x=cosec a/3
x^2=cosec^2 a/9

3/x=cot a
1/x=cot a/3
1/x^2=cot^2 a/9

3 (x^2-1/x^2 )=3 (cosec^2a/9-cot^2a/9)
=3((cosec^2 a-cot^2 a)/9)
=3(1/9) =1/3
(since, cosec^2 a-cot^2 a=1)