How do you find the solutions to sin^-1x=sin^-1(1/x)?

2 Answers
Ratnaker Mehta
Aug 22, 2016

The Soln. is x=+-1.

Explanation:

sin^-1x=sin^-1(1/x)

rArr sin(sin^-1x)=sin(sin^-1(1/x)

rArr x=1/x

rArr x^2=1

rArr x=+-1

These roots satisfy the given eqn.

Hence, the Soln. is x=+-1.

Nghi N.
Aug 22, 2016

pi/2, (3pi)/2

Explanation:

arcsin x = arcsin (1/x)
The 2 solutions are:
sin x = 1, and sin (1/x) = 1
sin x = - 1 , and sin (1/x) = - 1
Any other values of x will make the equations untrue.
a. sin x = 1 --> arc x = pi/2
b. sin x = - 1 --> arc x = (3pi)/2
Answers for (0, 2pi)
pi/2, (3pi)/2
Check
arc x = pi/2 --> arcsin (1) = arcsin (1/1)
arc x = (3pi)/2 --> arcsin (-1) = arcsin (1/-1)

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