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The set of values of x for which tan3x-tan2x/1+tan3xtan2x=1 is

The set of values of x for which tan3x-tan2x/1+tan3xtan2x=1 is 

Grade:12

10 Answers

Radhika Batra
247 Points
8 years ago

WE KNOW 

tanx = tan(3x-2x) = (tan3x - tan2x)/(1+tan3xtan2x)

therefore the above problem reduce to 

tanx=1

then find x.

Kevin Nash
askIITians Faculty 332 Points
8 years ago

(tan 3x - tan 2x) / (1 + tan 3x tan 2x) = tan (3x-2x) = tan x

So the equation becomes tan x = 1 = tan (pi/4)

Whose general solution is x = n*pi + pi/4 = (n+1/4) * pi

Kaushik
28 Points
8 years ago

tan(3x-2x)=1

tanx=1

x=n*pi + (pi/4)


jitender lakhanpal
62 Points
8 years ago

hi pavan

the Kaushik is correct

you just have to apply tan ( A - B ) formula

tan (A-B) = (tanA   -    tan B )/(1 - tanA  tan B  )

take A = 3 x and B = 2x

jitender

askiitians expert

Amit Nardiya
35 Points
7 years ago
We know that tan (A - B) = (tan A- tan B) / (1+ tan A. tanB) So (tan3x - tan2x) / (1+ tan3x tan2x) = tan (3x - 2x) = tan x So we have to find solution of tan x = 1 So x = p / 4 will 1 solution and x = np + p/4 will be general solution of equation. Thanks & Regards, Amit Nardiya, askIITians faculty.
rakib ansari
35 Points
7 years ago
We know that tan (A - B) = (tan A- tan B) / (1+ tan A. tanB) So (tan3x - tan2x) / (1+ tan3x tan2x) = tan (3x - 2x) = tan x So we have to find solution of tan x = 1 So x = p / 4 will 1 solution and x = np + p/4 will be general solution of equation.
Harsh Srivastava
34 Points
7 years ago
The answer for the given question is phi (?) or a null set.. tan (A - B) = (tan A- tan B) / (1+ tan A. tanB) So (tan3x - tan2x) / (1+ tan3x tan2x) = tan (3x - 2x) = tan x So we have to find solution of tan x = 1 So x = p / 4 will 1 solution and x = np + p/4 will be general solution of equation. But if x= p / 4 then, 2x= p / 2. And tan2x will not be defined.. You can check for other values of x as well...So The answer is phi (?) or a null set.
Shreyas V S
17 Points
3 years ago
The answer to this question is there is no set of solutions for this question, because if we take x=π/4 then if we substitute it in the equation we get an indefinite form of (infinity/infinity).... Hence there is no solution to this answer
Suhas
13 Points
3 years ago
Actually the answer is nullset.or pi.
Tan3x-tan2x/1+tan3x2x 
=tan(3x-2x)= tanx =1
x=pi/4i
Then if u substitute the value pi/4 , then
(Tan3(pi/4)-tan2(pi/4))/ 1-tan3(pi/4)tan2(pi/4)
Then the terms containing tan2(pi/4) becomes 
Tan2(pi/2) in the numerator and in the denominator so the  numerator and the denominator becomes infinity as tan(pi/2) is infiniy or not defined so the values of x is null set or phi.
tan3(pi/4)-ta2(
 
bhanu reddy
13 Points
2 years ago
there is no solution.since  if x=45, tan(2x) is not defined.
but if we simplify we get tan(3x-2x)=1 which implies x has solution
 

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