Question

If `(1-tan theta)(1+tan theta)sec^2 theta+2^(tan^2 theta)=0` then in the interval `(-pi/2,pi/2),` the value of `theta` is

Answer 1

Given that `(1-tan theta) (1+tan theta) sec^(2) theta+2^(tan^(2) theta)=0`
or `(1- tan^(2) theta) (1+tan^(2) theta)+2^(tan^(2) theta)=0`
Let us put `tan^(2) theta=t`. Then
`(1-t) (1+t)+2^(t)=0" "or" "1-t^(2)+2^(t)=0`
It is clearly satisfied by `t=3`. thus, we get
`tan^(2) theta=3`
Therefore, `theta= pm pi//3` in the given interval.