Question

Şec^-1(x^2+1/x^2-1)
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Answer 1

Answer:

We know that sec^(-1) A = π - sec^(-1) A

Cos 2A = (1-tan^2 A)/(1+tan^2 A) and also

sec^(-1) x = cos^(-1) (1/x)

So sec^(-1) {(x^2 + 1)/(x^2 - 1)}

= sec^(-1) {-(1+x^2)/(1-x^2)

= π - sec^(-1) {(1+x^2)/(1-x^2)}

= π - cos^(-1) {(1-x^2)/(1+x^2)

Let x = tanA => A = tan^(-1) x

The above becomes

π - cos^(-1) {(1-tan^2 A)/(1+tan^2 A)

= π - cos^(-1) cos 2A = π - 2A = π - 2 tan ^(-1) x

hope it helps u ..:)

Step-by-step explanation: