0

Guest

Courses New

In triangle ABC a²sin2B - b²sin2A then find the value of it

In triangle ABC a²sin2B - b²sin2A then find the value of it

Grade:10

1 Answers

Arun
25750 Points
5 years ago
a²sin2B + b²sin2A = c²cotC/2 
4R².sin²A.sin2B + 4R².sin²B.sin2A = 4R².sin²C.cotC/2 
sin²A.sin2B + sin²B.sin2A = sin²C.cotC/2 
(1 - cos2A)/2.sin2B + (1 - cos2B)/2.sin2A = sin²C.cotC/2 
sin2B - cos2A.sin2B + sin2A - cos2B.sin2A = 2sin²C.cotC/2 
sin2A + sin2B - sin(2A + 2B) = 2sin²C.cotC/2 ( vì sin2A.cos2B + cos2A.sin2B = sin (2A +2B) 
sin2A + sin2B + sin2C = 2sin²C.cotC/2 
2sin(A + B)cos(A - B) + 2sinC.cosC = 2sin²C.cotC/2 
2sinC.[ cos(A - B) - cos(A + B) ] = 2sin²C.cotC/2 
2sinC.-2.sinA.sin(-B) = 2sin²C.cotC/2 
4sinA.sinB.sinC = 2sin²C.cotC/2 
2sinA.sinB = sinC.cotC/2 
2sinA.sinB = 2sinC/2.cosC/2.cosC/2 /sinC/2 
sinA.sinB = cos²C/2 
2sinA.sinB = 1 + cosC 
2sinA.sinB = 1 - cos(A + B) 
2sinA.sinB = 1 - cosA.cosB + sinA.sinB 
cosA.cosB + sinA.sinB = 1 
cos(A - B) = 1 
A = B A - B =0

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More