Question

If, tanA = n tanB, and sinA = m sinB then what is the value of cos^2 A ?

Answer 1

Answer:

Tan A = n tan B

sin A=m sinB

sin B = sin A / m --------------- (1)

tan A=sinA/cosA

cos A = sin A / tan A = m sin B / n tan B = m cos B / n

cos B = n cos A / m -------------- (2)

squaring and adding (1) and (2)

[sin^2 B + cos^2 B] = sin^2 A / m^2 + n^2 cos^2 A / m^2

1 = [1 - cos^2 A]/m^2 + n^2 cos^2 A / m^2

m^2 = 1 - cos^2 A + n^2 cos^2 A

cos^2 A [n^2 - 1] = [m^2 -1]

cos^2 A = [m^2 -1] / [n^2 - 1]