Question

a+b=90° then prove that sec a+cos b/sin a =tan a+2tan b

Answer 1

Answer:

Step-by-step explanation:

Given, LHS = root tan a tan b + tan a cot b/sin a sec b - sin^2 b/cos^2 a

     = root tan a tan(90-a) + tan a cot(90-a)/sin a sec(90-a) - sin^2(90-a)/cos^2 a

     = root tan a.cot a + tan a.tana/sin a.cosec a - cos^2 a/cos^2 a

     = root 1+tan^2 a/1 - 1

    = root tan^2 a

   = tan a