Question

If tan C = a/b, then prove that a sin C - b cos C/ a sin C +b cos C = a 2 - b 2 /a 2 + b 2

Answer 1

tan C =a/b,  so  sinC / cos C = a/b  or  sin C = a/ b cos C

substituting  in  the  expression,  we  get

LHS =  a* a/b cos C -  b cosC  / a * a/b cos C + b cos C

taking  cos C  common  from  numerator  and  denominator  and

simplifying,  we  get  a2 - b2 / a2 + b2 =  RHS