If tan inverse(x^2-y^2/x^2+y^2)=a then prove that dy/dx=x/y (1-tana/1+tana).

2 answers

Hint:
write equation as:
tan(a)=(x²-y²)/(x²+y²)
Cross multiply to eliminate denominators:
(x²+y²)tan(a)=(x²-y²)
Implicitly differentiate both sides
(2x+2yy')tan(a) = 2x-2yy'
Group terms and express y'(=dy/dx) in terms of x, y and tan(a) to get the required expression.
Thanku soo much
Similar Questions
  1. Verify/prove the following:(sinA+tanA)/(1+secA) = sinA ______________________________ tanu = 1+sinu-cos^2u/cosu(1+sinu)
    1. answers icon 1 answer
    1. answers icon 4 answers
  2. Prove the identity:tanA/secA+1 = secA-1/tanA Can u please explainit to me step by step? I greatly appreciate your help! Thanks:)
    1. answers icon 2 answers
    1. answers icon 1 answer
more similar questions