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

Options

A. 2
B. 4
C. 0
D. 1

Answer

A

Explanation

`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.