Question

answer the above question... plzz... it's urgent...

Answer 1

hey mate

here's the solution....

Answer 2

Given : a sec Ф + b tan Ф + c = 0    ----- (1)

Given : p sec Ф + q tan Ф + r = 0    ------ (2)

(i)

On solving (1) * q & (2) * b, we get

⇒ aq sec Ф + bq tan Ф + cq = 0

⇒ bp sec Ф + bq tan Ф + rb = 0

  --------------------------------------------

   (aq - bp)secФ + cq - rq = 0

   (aq - bp)secФ = rb - cq

   secФ = (rb - cq)/aq - bp.

(ii)

On solving (1) * p & (2) * a, we get

⇒ ap sec Ф + bp tan Ф + cp = 0

⇒ ap sec Ф + aq tan Ф + ar = 0

   -------------------------------------------

                      (bp - aq)tanФ + (cp - ar) = 0

                        tan Ф = (ar - cp)/bp - aq.

Now,

We know that Sec^2 Ф - tan^2 Ф = 1.

⇒ [rb - cq/aq - bp]^2 -  [ar - cp/bp - aq]^2 = 1

⇒ [rb - cq/aq - bp]^2 - [cp - ar/aq - bp]^2 = 1

⇒ (rb - cq)^2 - (cp - ar)^2 = (aq - bp)^2

Therefore, the answer is (aq - bp)^2 - Option (B).

Hope this helps!