Question

If sec A-tan A=1/3, find the value of sec A and tan A.

Answer 1

we know that 
sec^2A - tan^2A = 1
(secA-tanA)(secA+tanA)=1
it is given that  secA-tanA=1/3  .......(1)
so                    secA+tanA=3     .......(2)
adding eqns (1) and (2)
   2secA=3+1/3
    2secA=10/3
  secA=5/3  ans
now putting in eqn (2)
tanA=3-(5/3)
tanA=4/3  ans

Answer 2

It's given that
sec A - tan A = 1/3                                                        (i)
we know that sec² A - tan² A = 1
⇒ (sec A + tan A)(sec A - tan A) =1
⇒ (sec A + tan A)*(1/3) = 1
⇒ (sec A + tan A) = 3                                                    (ii)
solving (i) and (ii)
we get 
sec A= 5/3
tan A= 4/3

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