Question

If Sec a -tan a=p Show that sec a=1/2(p+1/p) and tan a=1/2(1/p-p)

Answer 1

it's the solution of your question
and you can do the 2nd part your self by this

Answer 2

♧♧HERE IS YOUR ANSWER♧♧

Given that :

sec a - tan a = p .....(i)

We know that :

sec²a - tan²a = 1

=> (sec a + tan a)(sec a - tan a) = 1

=> (sec a + tan a) × p = 1

=> sec a + tan a = 1/p .....(ii)

Now, adding (i) and (ii) no. equations, we get :

2 sec a = p + 1/p

=> sec a =  ½(p + 1/p)

Again, subtracting (i) from (ii) no. equation, we get :

2 tan a = 1/p - p

=> tan a =  ½(1/p - p)

Therefore,

sec a =  ½(p + 1/p) and tan a =  ½(1/p - p).

(Proved)

♧♧HOPE THIS HELPS YOU♧♧