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What is the value of (tan x +2 tan 2x)/tan x ?

What is the value of (tan x +2 tan 2x)/tan x ?

Grade:11

4 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

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).

Arnab Mandal
18 Points
9 years ago

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
290 Points
9 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
290 Points
9 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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