Solution Let x = sec θ, then 
2
1
x − = 
sec2
1
θ − =tan
θ
Therefore, 
–1
12
cot
1
x −
= cot–1 (cot θ) = θ = sec–1 x, which is the simplest form EXERCISE 2 2
Prove the following:
1 3sin–1 x = sin–1 (3x – 4x3), 
1
1
–
2,
2
x


∈



2