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`