A problem in trigonometry If \tan(x+y) =a+b and \tan(x-y)=a-b Then prove that: a

Laura Jenkins

Laura Jenkins

Answered question

2022-03-02

A problem in trigonometry
If tan(x+y)=a+b and tan(xy)=ab Then prove that: atan(x)btan(y)=a2b2
I have used the formulae for tan(x+y) and tan(xy) and then cross multiplied and then found a and b individually and then tried to put the values of a and b in "atan(x)btan(y)"(l.h.s) but it did not lead to the r.h.s.

Answer & Explanation

aksemaktjya

aksemaktjya

Beginner2022-03-03Added 6 answers

In addition to David's: Let u=tanx  and  v=tany. You have
u+va+b=1uvanduvab=1+uv
What if you add two equations:
u+va+b+uvab=1uv+1+uv=2
(ab)(u+v)+(a+b)(uv)=2(a2b2)
Miles Martin

Miles Martin

Beginner2022-03-04Added 6 answers

hint....for simplicity write x for tanx and y for tany then eliminate xy from the pair of equations
x+y1xy=a+b
and
xy1+xy=ab

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