Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

JEE Class main Answered

Sir pls solve the following.
question image
Asked by rsudipto | 05 Jan, 2019, 09:17: AM
answered-by-expert Expert Answer
Let a = tan α, b = tan β and c = tan γ.
 
if a,b,c are roots of cubic eqn, then (x-a)(x-b)(x-c) = 0    or   x3 -(a+b+c)x2 +(ab+bc+ca)x -abc  = 0  ..................(1)
 
Given eqn. : x3 - p x2 - r = 0  ...........................(2)
 
hence by comparing eqn.(1) and (2) , we have
 
a+b+c = tanα + tanβ + tanγ = p ...................................(3)
 
ab + bc + ca = tanα tanβ + tanβ tanγ + tanγ tanα = 0 ..............................(4)
 
abc = tanα tanβ tanγ = r ......................................(5)
 
(1+tan2α)(1+tan2β)(1+tan2γ) = 1+(tan2α + tan2β + tan2γ ) + (tan2α tan2β + tan2β tan2γ +tan2γ tan2α) + ( tan2α tan2β tan2γ ) ................(6)
 
(tan2α + tan2β + tan2γ ) = ( tanα + tanβ + tanγ )2 - 2(tanα tanβ + tanβ tanγ + tanγ tanα) = p2 ..........................(7)
 
(tan2α tan2β + tan2β tan2γ +tan2γ tan2α) = (tanα tanβ + tanβ tanγ + tanγ tanα)2 - 2(tanα tanβ tanγ)(tanα + tanβ + tanγ) = -2pr ................(8)
 
Using eqn.(7) and eqn.(8), eqn(6) is written as : (1+tan2α)(1+tan2β)(1+tan2γ) = 1 + p2 -2pr +r2 = 1+(p-r)2
 
Answered by Thiyagarajan K | 09 Jan, 2019, 11:07: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
JEE main - Maths
maths sum
question image
Asked by keerthananukala2007 | 02 May, 2024, 11:32: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
the probability of attending a conference is 0.5, and the probability of attending a workshop is 0.3. if 40% of conference attendees also attend workshops, what is the probability that a student attends a workshop given that they attended a conference?
Asked by ms9876tr | 28 Apr, 2024, 12:05: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
a+bx e power of y/x =x then d square y by dx square
Asked by jameelmohd765 | 27 Apr, 2024, 10:23: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
find
question image
Asked by komuravellysravanthi4 | 26 Apr, 2024, 02:14: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
solution please
question image
Asked by piyurawriya | 24 Apr, 2024, 12:46: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
answer
question image
Asked by piyurawriya | 23 Apr, 2024, 02:02: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
let M be the skew symmetric orthogonal real matrix.Then only possible eigen values are
Asked by kakumanumanoj282 | 20 Apr, 2024, 06:07: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
sin-1(sin5π/3)
Asked by nirmalraulji5 | 18 Apr, 2024, 09:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
1
question image
Asked by hadiabbas803 | 17 Apr, 2024, 07:36: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
Cos66+sin84
Asked by veerababukoppisettiveerababu3 | 17 Apr, 2024, 05:49: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×