Question

If sec A + tan A = x, then sec A​

Answer 1

We are given , SecA+TanA=x ------- (1) equation

We know that Sec2A-Tan2A=1

This is of the form a2-b2=(a+b)(a-b)

So (SecA-TanA)(SecA+TanA)=1

SecA-TanA=1/x {From eq.1}

So Sec A - Tan A = 1 / x ---Lets consider this as Equation 2

Now adding Eq.1 and Eq.2,

we get 2SecA=x+1/x

Hence SecA=(x+1/x)/2

So SecA=(x2+1)/2x Answer.