Question

If x=a sec and y=b tan then prove that x^2/a^2-y^2/b^2=1

Answer 1

$\frac{x {}^{2} }{a { }^{2} } - \frac{y {}^{2} }{b {}^{2} }$
Substituting values of X and y

$\frac{a {}^{2} \sec {}^{2} ( \alpha ) }{a {}^{2} } - \frac{b {}^{2} \tan {}^{2} ( \alpha ) }{b {}^{2} } \\ \\ = \sec {}^{2} ( \alpha ) - \tan {}^{2} ( \alpha )$
We know that sec² X - tan² X = 1 ( Trigonometric identities )

so,

$\sec {}^{2} ( \alpha ) - \tan {}^{2} ( \alpha ) = 1$


Hence proved!!!!