Prove that: tan²A -tan²B = {sin(A+B).sin(A-B)}/ cos²A.cos²B 
 Answer:

Okay, so this question is kind of irritating one because it has so much repeated processes in the solution. But don't worry. We are here to help you. First of all, you need to know the formula of Compound Angles to start the solution as given sin(a+b) and sin(a-b) have their own Trigonometric expansions. Then you can perform the basic Mathematics and then you will get yourself in a state where you can cancel the denominator and numerator and prove the Trigonometric values by showing that the right hand side is equal to the left hand side of the question.
Remember,
Tan x= sinx/ cosx
Tan y= siny/cosy

Have a look at these formulas:


So, with all these steps, tricks and processes in mind, you will be able to completely solve this question.

#SciPiTutor
#CompoundAngles
#Trigonometry
#Mathematics