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tan(A+B)- tan(A-B)= sin 2B/cos square B- sin square A

tan(A+B)- tan(A-B)= sin 2B/cos square B- sin square A

Grade:11

2 Answers

Anish Singhal
askIITians Faculty 1194 Points
3 years ago
Please write question properly
Soumendu Majumdar
159 Points
3 years ago
Dear Student,
Before proceeding let's give you a hint of the formulas you will require to solve this question
  1. sin(A+B)cos(A-B) – sin(A-B)cos(A+B) = sin 2B
  2. 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!

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