Question

tan a+ sin a= m and tan a - sin a = n show that m2 - n2= root mn

Answer 1

Answer:

Here

m2 – n2 = (tan A + sin A)2 – (tan A – sin A)2

= (tan A + sin A + tan – sin A)(tan A + sin A – tan A + sin A)

= (2 tan A)(2 sin A)

= 4 tan A sin A …..(1)

Also

= 4 sin A. sin A/cos A

= 4 sin A. tan A …..(2)

Using eq. (1) and eq. (2) we get the required conditions.

Hence Proved