Question

IF X = A SEC θ + B TAN θ AND Y = A TAN θ + B SEC, PROVE THAT X2 - Y2 = A2 - B2

Answer 1

This is your answer

Answer 2

X^2= A^2sec^2θ + 2ABsecθtanθ + B^2tan^2θ           (1`)
 
Y^2= A^2tan^2θ + 2ABsecθtanθ +  B^2sec^2θ            (2)
    
 subtracting equation 1 and 2
  
X^2-Y^2=  A^2(sec^2θ-tan^2θ) + B^2 (tan^2θ-sec^2θ)


X^2-Y^2=  A^2(sec^2θ-tan^2θ) - B^2 (sec^2θ-tan^2θ)      (3)
  


By identity
sec^2θ= 1+ tan^2θ

IN eqn 3 we get X^2 -Y^2 = A^2-B^2 
hence proved