Question

If a = x seco + y tane , b = x tan +ysec e then x2-y2 =​

Answer 1

$given \: that \\ a = x \: sec \theta + y \: tan \theta \: \: \: eqn(i) \\ b = x \: tan \theta \: + y \: sec \theta \: \: \: \: eqn(ii)$

$to \: find \\ {x}^{2} - {y}^{2}$

squaring eqn(I) and (II) and then subtracting eqn (ii) from (i)

${a}^{2} - {b}^{2} = {(x \: sec \theta + y \: tan \theta) }^{2} - {(x \: tan \theta + y \: sec \theta) }^{2}$

➹Now refer to the attachment➷

So, we get the answer that,

${x}^{2} - {y}^{2} = {a}^{2} - {b}^{2}$

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