In any ΔABC, prove that a sin A – b sin B = c sin (A

Home » In any ΔABC, prove that a sin A – b sin B = c sin (A – B)

In any ΔABC, prove that a sin A – b sin B = c sin (A – B)

RS Aggarwal Class 11 Maths Solution of Triangles

In any ΔABC, prove that a sin A – b sin B = c sin (A – B)

: Need to prove: a sin A – b sin B = c sin (A – B)
Left hand side,
= a sin A – b sin B
= (b cosC + c cosB) sinA – (c cosA + a cosC) sinB
= b cosC sinA + c cosB sinA – c cosA sinB – a cosC sinB
= c(sinA cosB – cosA sinB) + cosC(b sinA – a sinB)