1.

The number of values of `theta`in the interval `(-pi/2,pi/2)`satisfying the equation `(sqrt(3))^(sec^2theta)=tan^4theta+2tan^2theta`is2 (b)4 (c) 0(d) 1A. 2B. 4C. 0D. 1

Answer» Correct Answer - A
`tan^(4) theta+2 tan^(2) theta=(tan^(2) theta+1)^(2)-1=(sec^(2) theta)^(2) -1=sec^(4) theta-1`
Puutting `sec^(2) theta=t` we get
`(sqrt(3))^(t)=t^(2)-1`
`rArr t=2` is the only solution as `t gt 1`
Hence, there will be 2 values of `theta` in given interval.


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