1800-150-456-789
FlagBACK
Flag Trigonometry> Prove that in any triangle tan B-C = b-c ...
question mark

Prove that in any triangle
tanB-C = b-c cotA/2
2 b+c

Bil , 9 Years ago
Grade 11
anser 3 Answers
BALAJI ANDALAMALA

Last Activity: 9 Years ago

511-2439__20160112_173229.JPG

Rp mahaveer

Last Activity: 7 Years ago

Consider b-c/b+c=2RSINB-2RSINC/2RSINB+2RSINC = 2R (SINB-SINC)/(SINB+SINC) =2COS(B+C/2)×SIN(B-C/2)/2SIN(B+C/2)×COS(B-C/2) =COT (B+C/2)×TAN(B-C/2)=COT (90°-A/2)×TAN (B-C/2)=TANA/2×TAN(B-C/2)TAN(B-C/2)=B-C/B+C×COT(A/2)

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the solution to your problem.
 
Consider b-c/b+c
= 2RsinB – 2RsinC/2RsinB + 2RsinC
= 2R(sinB – sinC)/(sinB + sinC)
= 2cos(B + C/2) × sin(B – C/2)/2sin(B + C/2) × cos(B – C/2) = cot(B + C/2) × tan(B – C/2)
= cot(90° – A/2) × tan(B – C/2)
= tanA/2 × tan(B – C/2)
Hence, tan(B – C/2) = b-c/b+c × cot(A/2)
 
Thanks and regards,
Kushagra

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free

Other Related Questions on trigonometry

question mark
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
1 Answer Available

Last Activity: 2 Years ago

question mark
  • Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
To prove : Cosec(45 degree - A)Cosec(45 degree + A) = 2SecA
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
cos^2 13ºcos^2 47º+cos^2 73º =? …..................
trigonometry
0 Answer Available

Last Activity: 3 Years ago

question mark
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
0 Answer Available

Last Activity: 3 Years ago