in triangle ABC , prove that b^2 sin2C + c^2 sin2B = 2bc sinA - Maths - Trigonometric Functions

Question

in triangle ABC , prove that b^2 sin2C + c^2 sin2B = 2bc
sinA

Ajanta Trivedi · Accepted Answer

LHS of the given equation is:
b2sin2C+c2sin2B=b2 2sinCcosC+c2
2sinBcosB  [since sin2θ=2sinθ cosθ=2
b2sinCcosC+c2sinBcosB=2 b2 Kc a2+b2-c22ab+c2 Kb
a2+c2-b22ac   [by sine rule :sinCc=sinBb=sinAa=K=2Kbc
a2+b2-c22a+a2+c2-b22a     [by cosine rule :cosC=a2+b2-c22ab=2Kbc
a2+b2-c2+a2+c2-b22a=2Kbc 2a22a=2Kabc
=2bc (Ka)=2bc sinA=RHS

hope this helps you