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What is the value of (tan x +2 tan 2x)/tan x ?
Hi Arnab,
tan2x = 2tanx/(1+tan^2x)
Substitute for tan2x and simplify,
The given expression = 1 + 4/(1+tan^2 x)
= [tan^2 x + 5] / [ tan^2 x + 1 ]
Hope that helps.
Best Regards,
Ashwin (IIT Madras).
First of all tan 2x = 2tan x/1-tan^2x. And the options given are a) less than 1, b)greater than 5, c)is between 1 and 5, d)is less than 1 or greater than 5. Now please rectify and find the answer.
The above expression is of the form (Say tanx = t)
[ t^2 + 5 ] / [t^2 + 1] = 1 + 4/(t^2 + 1)
So it is always greater than 1, and the maximum value occurs when the denominator is minimum, ie when t = 0, for which the value is 5.
Hence it lies between 1 and 5.
Extremely sorry for that silly mistake.
Yes tan2x = 2tanx/(1-tan^2 x)
So the expression is 1 + 4/(1-t^2) ------(where t is tanx).
Hence the expression is greater than 5, when 0 <= t^2 < 1.
When t>1, the expression is less than 1.
So the given expression is greater than 5 or less than 1.
Hope this helps.
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