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.
Ashwin Muralidharan IIT Madras
Last Activity: 13 Years ago
Hi Arnab,
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.
Hope that helps.
Best Regards,
Ashwin (IIT Madras).
Ashwin Muralidharan IIT Madras
Last Activity: 13 Years ago
Hi Arnab,
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.
Best Regards,
Ashwin (IIT Madras).
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