Question

) if m= a Sec A +b tan A n=a tan A+ b Sec A then prove that m2-n2=a2-b2​

Answer 1

m²-n²=(m+n)(m-n)    

  ={(a sec A+ b tan A)+ (a tan A+ b sec A)}{(a sec A+ b tan A)-(a tan A+ b sec A)}

  ={(a+b) sec A+(a+b) tan A}*{(a-b) sec A- (a-b) tan A}

  =(a+b)(sec A+ tan A)*(a-b) (sec A -tan A)

  = (a+b) (a-b) (sec A +tan A)(sec A- tan A)

  =(a²-b²)(sec²A-tan²A)

  =(a²-b²)(1+tan²A-tan²A)

  =a² - b²