Question

If `sec theta = 5/4`, find the value of `(sin theta - 2 cos theta)/(tan theta - cot theta)`

Answer 1

We have `sec theta= 5/4`

In ΔABC

`AC^2 = AB^2 + BC^2`

`=> (5)^2 = AB^2 + (4)^2`

`=> AB^2 = 25 - 16`

`=> AB = 3`

`∴ sin theta (AB)/(AC) = 3/5, cos theta = 4/5, tan theta =3/4, cot theta = 3/4`

Now

`(sin theta - 2 cos theta)/(tan theta - cot theta) = (3/5 -  2 xx 4/5)/(3/4 - 4/3)`

`= 1/5 xx (3-8)/((9 - 16)/12)`

`= 1/5 xx (-5/7)xx12`

`= 12/7`