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2tan^2x+sec^2x=2 for 0ltxlt2pi...

`2tan^2x+sec^2x=2` for `0ltxlt2pi`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Here , `2tan^(2)x+sec^(2)x=2`
`rArr2tan^(2)x+1+tan^(2)x=2rArr3tan^(2)x=1`
which gives tan `x=+-(1)/(sqrt(3))`
If we take tan x `=(1)/(sqrt(3))"then "x=(pi)/(6)or(7pi)/(6)`
Again , if we take tan x `x=(-1)/(sqrt(3)),"then " x=(5pi)/(6)or(11pi)/(6)`
Therefore ,the possible solutions of above equations are
`x=(pi)/(6),(5pi)/(6),(7pi)/(6)and(11pi)/(6), "where"0lexle2pi`.
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