Ask a Doubt
Request a call back

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

JEE Class main Answered

If A+B+C=180°, then prove that tan^2theta/2=tanB/2tanC/2, when costheta(sinB+sinC)=sinA
Asked by azizrajil03 | 01 Mar, 2019, 06:26: AM
answered-by-expert Expert Answer
begin mathsize 12px style G i v e n space colon space space cos theta space equals space fraction numerator sin space A over denominator sin space B space plus space sin space C end fraction space equals space fraction numerator sin left square bracket space 180 space minus left parenthesis B plus C right parenthesis space right square bracket over denominator sin space B space plus space sin space C end fraction space equals space fraction numerator sin space left parenthesis B plus C right parenthesis over denominator sin space B space plus space sin space C end fraction h e n c e space s e c space theta space equals space fraction numerator sin space B space plus space sin space C over denominator sin space left parenthesis B plus C right parenthesis end fraction space equals space fraction numerator sin B over denominator sin open parentheses B plus C close parentheses end fraction space plus space fraction numerator sin C over denominator sin open parentheses B plus C close parentheses end fraction space space................... left parenthesis 1 right parenthesis fraction numerator sin B over denominator sin left parenthesis B plus c right parenthesis end fraction space equals space fraction numerator sin B over denominator sin B space cos C plus cos B sin C end fraction space equals space fraction numerator begin display style bevelled fraction numerator 2 tan space begin display style B over 2 end style over denominator 1 plus tan squared begin display style B over 2 end style end fraction end style over denominator begin display style fraction numerator 2 tan begin display style B over 2 end style open parentheses 1 minus tan squared begin display style C over 2 end style close parentheses over denominator open parentheses 1 plus tan squared begin display style B over 2 end style close parentheses space open parentheses 1 plus tan squared C over 2 close parentheses end fraction end style space plus space fraction numerator 2 tan begin display style C over 2 end style open parentheses 1 minus tan squared begin display style B over 2 end style close parentheses over denominator open parentheses 1 plus tan squared begin display style B over 2 end style close parentheses space open parentheses 1 plus tan squared C over 2 close parentheses end fraction end fraction fraction numerator sin space B over denominator sin left parenthesis B plus c right parenthesis end fraction space equals space fraction numerator 2 tan space B over 2 over denominator fraction numerator 2 tan begin display style B over 2 end style open parentheses 1 minus tan squared begin display style C over 2 end style close parentheses over denominator space open parentheses 1 plus tan squared C over 2 close parentheses end fraction space plus space fraction numerator 2 tan begin display style C over 2 end style open parentheses 1 minus tan squared begin display style B over 2 end style close parentheses over denominator space open parentheses 1 plus tan squared C over 2 close parentheses end fraction end fraction space equals space fraction numerator t a n space B over 2 space open parentheses 1 plus tan squared C over 2 close parentheses over denominator tan B over 2 open parentheses 1 minus tan squared C over 2 close parentheses plus tan C over 2 open parentheses 1 minus tan squared B over 2 close parentheses end fraction space........... left parenthesis 2 right parenthesis S i m i l a r l y space w e space c a n space p r o v e space fraction numerator sin space C over denominator sin left parenthesis B plus c right parenthesis end fraction space equals space space fraction numerator t a n space C over 2 space open parentheses 1 plus tan squared B over 2 close parentheses over denominator tan B over 2 open parentheses 1 minus tan squared C over 2 close parentheses plus tan C over 2 open parentheses 1 minus tan squared B over 2 close parentheses end fraction space space............... left parenthesis 3 right parenthesis B y space u sin g space e q n. left parenthesis 2 right parenthesis space a n d space e q n. left parenthesis 3 right parenthesis comma space space space e q n. left parenthesis 1 right parenthesis space c a n space b e space w r i t t e n space a s s e c space theta space equals space space fraction numerator t a n space B over 2 space open parentheses 1 plus tan squared C over 2 close parentheses space plus space t a n space C over 2 space open parentheses 1 plus tan squared B over 2 close parentheses over denominator tan B over 2 open parentheses 1 minus tan squared C over 2 close parentheses plus tan C over 2 open parentheses 1 minus tan squared B over 2 close parentheses end fraction space equals space fraction numerator 1 plus tan B over 2 space tan C over 2 over denominator 1 minus tan begin display style B over 2 end style tan begin display style C over 2 end style end fraction c os space theta space equals space fraction numerator 1 minus tan squared begin display style theta over 2 end style over denominator 1 plus tan squared theta over 2 end fraction space equals space fraction numerator 1 minus tan B over 2 tan C over 2 over denominator 1 plus tan B over 2 tan C over 2 end fraction space space space space space o r space space tan squared theta over 2 space equals space tan B over 2 tan C over 2 end style
Answered by Thiyagarajan K | 01 Mar, 2019, 12:32: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
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
JEE main - Maths
how to solve this in financial calculator by log
question image
Asked by usakoyalshailesh | 15 Apr, 2024, 09:48: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
dout
question image
Asked by satnamk123 | 15 Apr, 2024, 01:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
I am not able to get the idea for solving this question I know properties of det.
question image
Asked by sharmalalita847 | 14 Apr, 2024, 09:21: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
A∆B=AUB/A'UB'
Asked by sarthakshukla7275 | 14 Apr, 2024, 01:29: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
JEE main - Maths
how to solve this complex number problem
question image
Asked by ashwinskrishna2006 | 14 Apr, 2024, 11:58: AM
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
×