Question

tan =a/b then prove that a sin - b cos/ a sin + b cos = a^2 - b ^2 / a^2 +b^2

Answer 1

LHS = (a sinx - b cosx )/(a sinx + b cosx )

now, divide by cosx both numerator and denominator .

= (a sinx/cosx - b cosx/cosx )/(a sinx/cosx + b cosx/cosx )
= (a tanx - b)/(a tanx + b)

now, put tanx = a/b

= (a × a/b - b )/(a × a/b + b )
= (a² - b²)/(a² + b² ) = RHS