Question

if ½<|x|<1,then which of the following is/are real?


option a :- sin^-1 x

option b :- tan^-1 x

option c :- cos^-1 2x

option d :- cos^-1 x

MORE THAN ONE OPTION CAN SELECTED​

Answer 1

Answer:

Correct option is

A

sin−1x

B

tan−1x

D

cos−1x

∣x∣<1 implies

−1<x<1

x∈(−1,1)

21<∣x∣

x>21 and x<2−1

x∈(−∞,2−1)∪(21,∞)

Taking the intersection, we get the solution set for the above inequality as

x∈(−1,2−1)∪(21,1)

Hence x is real for sin−1(x), tan−1(x) and cos−1(x).