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Question
Solve 2 tan2x + sec2x = 2 for 0 ≤ x ≤ 2π.
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Solution
Here, 2 tan2x + sec2x = 2
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 = `(-1)/sqrt(3)`
Then x = `(5pi)/6` or `(11pi)/6`
Therefore, the possible solutions to the above equations are
x = `pi/6, (5pi)/6, (7pi)/6` and `(11pi)/6` where 0 ≤ x ≤ 2π.
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