JEE Trigonometry 1
If tan θ , 2 tan θ + 2 , 3 tan θ + 3 are in a geometric progression , then the value of 9 tan θ + 4 tan θ cos 2 θ 1 − 1 7 tan θ − 5 is X . Calculate ⌊ 1 0 0 X ⌋
This problem is a part of My picks for JEE 2
The answer is 33.
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2 solutions
Well, I don't think 33 is the only answer to this problem! Anyone feeling same?
4 ( 1 + tan x ) 2 = 3 tan x ( 1 + tan x )
( 1 + tan x ) ( 4 + 4 tan x − 3 tan x ) = 0
P o s s i b i l i t i e s tan x = − 1 o r tan x = − 4
Checking for the values ,
for tan x = − 1 , a G . P i s n o t f o r m e d s o o n l y o n e v a l u e o f tan x t h u s o n l y o n e a n s w e r
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At tanx=-1 GP is formed. Tanx=-1, 2tanx +2=0, 3tanx+3=0. For GP (tanx)(3tanx+3)=(2tanx+2)^2. (-1)(0)=(0)^2.
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OK so your are confused , according to you for tanx = -1 G.P is formed ( lets consider it true for this point of time)
So our terms will be − 1 , 0 , 0
Common ratio = a 1 a 2 = − 1 0 = 0
Common ratio = a 2 a 3 = 0 0 = ? ? ? ?
thus G.P cannot be formed with 0 as one of its terms. Thanks
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@U Z – Ok thanks..but just one more doubt. What if I write, ((1/cosx)^2 -1) as (tanx)^2. Then the denominator would be 9tanx+4(tanx)^2. Now put tanx=-4, answer won't come out to be 33.
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@Bhavesh Ahuja – Denominator would be 9 tan θ + 4 tan θ ∣ tan θ ∣ .
Do you think ( − 9 ) 2 = − 9 ?
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@Pranjal Jain – Thanks @megh choksi for clarifying the case of tan θ = − 1 ⌣ ¨
See the answer can also be 117. As |tanx| = 4 also. So the denominator can be 9tanx + 4tan^2x .
Please explain!!!!
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( cos 2 θ ) 1 − 1 = 4 and not tan θ .
yes,i also had 117 as my answer
Bhavesh Ahuja if you have a doubt rather than asking it - i.e posting it as a solution you can click the .... button , and submit a dispute.
The problem has been wrongly stated it should have read as (7Tan A-5)/(9TanA-4TanA(1/CosA^2-1)^(1/2). Where A stands for theta. I am unable to write Theta as a symbol with my keyboard. Now if the GP is solved and tan=-4 will imply 100*X answer is 33. Hence there is error in writing the problem
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The problem isn't wrongly stated.
No I think the wordings are right , see only for one value of theta the G.P is formed
Please use LaTeX .
The problem has been wrongly stated. The denominator should read as 9Tan A-4TanA(CosA^-2-1)^(1/2). If this had been the case and then solving the GP and taking value as -4, 100*X =33. Please correct the problem.
Ya, I think the same. Other answer can be 92 as we have 2 values of tan(theta) -4 and -1.
No! It is not possible. Cause we cannot simplify the expression stated before placing the values.
As tan θ , 2 tan θ + 2 and 3 tan θ + 3 are in G.P. Hence tan θ 2 tan θ + 2 = 2 tan θ + 2 3 tan θ + 3 . From this tan θ = -4 . Substitute this value and get 33 as the answer . But take care that ( cos 2 θ ) 1 − 1 = 4 and not -4 .