Question

m tan (a-theta)÷cos ka scoured = n tan theta÷ cos ka squre (a-theta)

Answer 1

tan(m theta) = tan(n theta)

Take the inverse tangent of both sides:

m theta = N theta + pi N  for  N belongs to Z

Subtract b theta from both sides:

theta (m-n) = pi N  for  N belongs to Z

Divide both sides by m-n:

theta = (pi N)/(m-n)  for  N belongs to Z

so, putting value of N=1, theta=pi/(m-n)

putting value of N=2, theta=2pi/(m-n) and so on..

so the values of theta form an ap

and common difference = (N+1)pi/(m-n)-N pi/(m-n)=pi/(m-n)

Therefore,proved that values of theta form an AP with common difference pi/(m-n)

Hope this will help u.