IF x cos(alpha)+ ysin( alpha)=1, a b x cos(Beta) + y sin(Beta)=1 and a b cos(alpha)cos(Beta) + a 2 sin(alpha)sin(Beta) =0 then b 2 prove that: tan(alpha)tan(beta)={b 2 (x 2 - a 2 )}/{a 2 (y 2 - b 2 )}

IF x cos(alpha)+ ysin(alpha)=1,
    a                   b
xcos(Beta) + ysin(Beta)=1 and
a                  b
cos(alpha)cos(Beta)  +
sin(alpha)sin(Beta) =0 then
prove that:
  tan(alpha)tan(beta)={b2(x- a2)}/{a2(y2- b2)}


1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
9 years ago

Square the equation one and two on both sides and ADD and simplify.
You will see taht the expression of third equation will come up i the addition which will be zero.

Then take x^2 terms on one side and y^2 terms on other side and sipmlify.
You will get the result.

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