1800-150-456-789
FlagBACK
Flag Trigonometry> If A+B+C=180Prove that Sin^2A/2 +sin^2B/2...
question mark

If A+B+C=180Prove that Sin^2A/2 +sin^2B/2+sin^2C/2=1_2sinA/2sinB/2sinC/2

Eswari , 7 Years ago
Grade 11
anser 3 Answers
Vikas TU

Last Activity: 7 Years ago

Dear Student,
Taking LHS:
=Sin^2 A/2+sin^2 B/2+sin^2 C/2
=1-cos^2 A/2 +sin^2 B/2+sin^2 C/2
=1-(cos(A+B)/2 cos(A-B)/2) + sin^2 C/2
= 1-(cos(pi-C)/2 cos(A-B)/2)+sin^2C/2
= 1+sin C/2(sin C/2 -cos(A-B)/2)
=1+sin C/2(sin(pi –(A+B)/2 -cos(A-B)/2)
=1+sin C/2(cos (A+B)/2-cos(A-B)/2)
=1+sin C/2(-2sinA/2 sinB/2) = 1-2sinA/2 sin B/2 sin C/2 =RHS [hence proved].
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

Saurabh Singh

Last Activity: 6 Years ago

Given that :-Sin²a/2 + sin²b/2 + sin²c/2(1 - Cosa + 1- cosb +1 - cos c)/2(3 - ( Cosa +cosb + cosc))/2(3 -(1 +4 sin²a/2 sin²b/2sin²c/2))/2(2 - 4 sin²a/2 sin²b/2sin²c/2)/21-2sin²a/2 sin²b/2sin²c/2

Kushagra Madhukar

Last Activity: 4 Years ago

Dear student,
Please find the answer to your question.
 
Taking LHS:
=Sin^2 A/2+sin^2 B/2+sin^2 C/2
=1-cos^2 A/2 +sin^2 B/2+sin^2 C/2
=1-(cos(A+B)/2 cos(A-B)/2) + sin^2 C/2
= 1-(cos(pi-C)/2 cos(A-B)/2)+sin^2C/2
= 1+sin C/2(sin C/2 -cos(A-B)/2)
=1+sin C/2(sin(pi –(A+B)/2 -cos(A-B)/2)
=1+sin C/2(cos (A+B)/2-cos(A-B)/2)
=1+sin C/2(-2sinA/2 sinB/2) = 1-2sinA/2 sin B/2 sin C/2 =RHS [hence proved].
 
Thanks and regards,
Kushagra

Provide a better Answer & Earn Cool Goodies

Enter text here...
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

Enter text here...

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 Year ago(s)

question mark
\tFind the general solution of equation tan3∂=cot2∂For all angles between -720 and +720
Trigonometry
0 Answer Available

Last Activity: 2 Year ago(s)

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

Last Activity: 2 Year ago(s)

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

Last Activity: 2 Year ago(s)

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: 2 Year ago(s)