1800-150-456-789
FlagBACK
Flag Trigonometry> Prove that (sin a)+(sin b)+(sin c)-sin(a+...
question mark

Prove that (sin a)+(sin b)+(sin c)-sin(a+b+c)=4sin(a+b/2)sin(b+c/2)sin(a+c/2).

Durwa Thakur , 6 Years ago
Grade 11
anser 1 Answers
Sami Ullah

Last Activity: 6 Years ago

It looks quite difficult but its very easy if you try to solve it.It is pretty straight-forward.
 
L.H.S:-
 
=[\sin (a)+\sin (b)]+[sin(c)+sin(a+b+c)]
 
=[2sin(\frac{a+b}{2})cos(\frac{a-b}{2})]+[2cos(\frac{c+a+b+c}{2})sin(\frac{c-a-b-c}{2})]
 
=[2sin(\frac{a+b}{2})cos(\frac{a-b}{2})]+[2cos(\frac{a+b+2c}{2})sin(\frac{-(a+b)}{2})]
 
=[2sin(\frac{a+b}{2})cos(\frac{a-b}{2})]-[2cos(\frac{a+b+2c}{2})sin(\frac{(a+b)}{2})]
 
=2sin(\frac{a+b}{2})[cos(\frac{a-b}{2})]-cos(\frac{a+b+2c}{2})]
 
=2sin(\frac{a+b}{2})[-2sin(\frac{\frac{a-b+2c+a+b}{2}}{2})sin(\frac{\frac{a-b-2c-a-b}{2}}{2})]
 
=-4sin(\frac{a+b}{2})[sin(\frac{2a+2c}{4})]sin(\frac{-2b-2c}{4})]
 
=-4sin(\frac{a+b}{2})[sin(\frac{2(a+c)}{4})]sin(\frac{-2(b+c)}{4})]
 
=-(-4)sin(\frac{a+b}{2})[sin(\frac{a+c}{2})sin(\frac{b+c}{2})]
 
=4sin(\frac{a+b}{2})sin(\frac{a+c}{2})sin(\frac{b+c}{2})
 
I hope that awnsers your question.Actually I saw it today although you posted the question 11 days ago.Sorry for the delay.
 
 
 
 

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