Question

If `cot theta = 1/ sqrt(3) , "write the value of" ((1- cos^2 theta))/((2 -sin^2 theta))`

Answer 1

We have , 

 `cot theta = 1/ sqrt(3)`

  ⇒` cot theta = cot (π/3)`

  ⇒`theta = π/3`

 Now , 

     `((1- cos^2 theta))/((2 - sin^2 theta))`

    = `(1- cos ^2(π/3))/( 2 - sin ^2 ( π/ 3))` 

    =` (1- (1/2)^2)/(2-(sqrt(3)/2)^2)`

    =` ((1/1 - 1/4))/((2/1-3/4))`

    =`((3/4))/((5/4))`

    =`3/5`