JEE Advance - Mathematics (2005 - No. 18)
Find the range of values of $$\,t$$ for which $$$2\,\sin \,t = {{1 - 2x + 5{x^2}} \over {3{x^2} - 2x - 1}},\,\,\,\,\,t\, \in \,\left[ { - {\pi \over 2},\,{\pi \over 2}} \right].$$$
$$\left[ { - {\pi \over 2},{ - \pi \over 6}} \right] \cup \left[ {{\pi \over 6},{\pi \over 2}} \right]$$
$$\left[ { - {\pi \over 2},{ - \pi \over 3}} \right] \cup \left[ {{\pi \over 3},{\pi \over 2}} \right]$$
$$\left[ {{{ - \pi } \over 2},\,{{ - \pi } \over {10}}} \right]\, \cup \,\left[ {{{3\pi } \over {10}},\,{\pi \over 2}} \right]$$
$$\left[ { - {\pi \over 2},{\pi \over 2}} \right]$$
$$\left[ {0,{\pi \over 2}} \right]$$