IF X = A SEC θ + B TAN θ AND Y = A TAN θ + B SEC, PROVE THAT X2 - Y2 = A2 - B2
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Is that x square - y square?
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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
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
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