Question

prove that tan(a+b) - tan(a-b)= sin2b /cos^b - sin^2 a

Answer 1

Dear frnd,

Before proceeding let's give you a hint of the formulas you will require to solve this question

sin(A+B)cos(A-B) – sin(A-B)cos(A+B) = sin 2B

cos(A+B)cos(A-B) = cos^{2}B - sin^2A or cos^{2}A - sin^2B

Now tan(A+B) = sin(A+B)/cos(A+B)

tan(A – B) = sin(A – B)/cos(A – B)

so tan(A+B) – tan(A-B) = [ sin(A+B)cos(A-B) – sin(A-B)cos(A+B) ]/[ cos(A+B)cos(A-B) ]

= sin 2B / { cos^{2}B - sin^2A } [Proved]

Hope it helps!