Question

How do you solve the following equation `tan^2xsinx=tan^2x` in the interval [0, 2pi]?

Answer 1

The Soln. Set`={0,pi,2pi} sub [0,2pi]`.

Explanation:

`tan^2xsinx=tan^2xrArrtan^2xsinx-tan^2x=0`

`rArr(sinx-1)tan^2x=0rArr sinx=1, or, tan^2x=0`

But, `sinx=1rArr cosx=0, & so, tanx` will be undefined.

Therefore, `tan^2x=0rArrtanx=0rArrsinx=0rArr x=npi, n in ZZ`

`:. { x in [0,2pi] : sinx=0}={0,pi,2pi}`