29. Ifan A a tan B and sin A bain R, prove that coA-1ORProve that :

1.	29. Ifan A a tan B and sin A bain R, prove that coA-1ORProve that :
Answer» sinA = bsinB....(1) tanA= atanB (sinA/cosA) = a(sinB/cosB)....(2) substuting sinB value from equation (1) cosB = (a/b) cosA......(3) sin2A = b2sin2B 1-cos2A = b2(1-cos2B) substituting equation (3) 1-cos2A = b2[1 – ((a2/b2)cos2A)] 1 – cos2A = b2– a2cos2A a2cos2A – cos2A = b2– 1 cos2A = (b2– 1)/(a2– 1)

Answer»

sinA = bsinB....(1)

tanA= atanB

(sinA/cosA) = a(sinB/cosB)....(2)

substuting sinB value from equation (1)

cosB = (a/b) cosA......(3)

sin2A = b2sin2B

1-cos2A = b2(1-cos2B)

substituting equation (3)

1-cos2A = b2[1 – ((a2/b2)cos2A)]

1 – cos2A = b2– a2cos2A

a2cos2A – cos2A = b2– 1

cos2A = (b2– 1)/(a2– 1)

Discussion