Question

If tan A = ntan B, sin A = msin B, Prove that cos2A = (m2-1) / (n2-1)

Answer 1

sinA = msinB....(1)

tanA= ntanB

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

substuting sinB value from equation (1)

cosB = (n/m) cosA......(3)

sin2A = m2sin2B

1-cos2A = m2(1-cos2B)

substituting equation (3)

1-cos2A = m2[1 – ((n2/m2)cos2A)]

1 – cos2A = m2 – n2cos2A

n2cos2A – cos2A = m2 – 1

cos2A = (m2 – 1)/(n2 – 1)

Answer 2

Answer:

Here is step by step solution of your question