If `t a ntheta=a/b ,\ ` show that `(a\ sintheta-b costheta)/(\ a\ sintheta+b\ costheta)=(a^2-b^2)/(a^2+b^2)`

Explanation

Consider `\frac{a \sin \theta-b \cos \theta}{a \sin \theta+b \cos \theta}`


Take `\cos \theta` common fiom Numerator and Denominator
`\frac{\cos \theta(\frac{a \sin \theta}{\cos \theta}-b)}{\cos \theta(\frac{a \sin \theta}{\cos \theta}+b)}`
`=\frac{a \tan \theta-b}{a \tan \theta+b}`
`=\frac{a(\frac{a}{b})-b}{a(\frac{a}{b})+b}`
`=\frac{\frac{a^{2}-b^{2}}{b}}{\frac{a^{1}+b^{2}}{b}}`
`=\frac{a^{2}-b^{2}}{a^{2}+b^{2}}`

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