Math, asked by Hadiasharif, 1 year ago

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

Answers

Answered by BrainlyHulk
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!!!!

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