Inverse Circular Functions 1 Question 1

1. The number of real solutions of

tan1x(x+1)+sin1x2+x+1=π2 is 

(a) zero

(b) one

(c) two

(d) infinite

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Answer:

Correct Answer: 1. (c)

Solution:

  1. Given function is

tan1x(x+1)+sin1x2+x+1=π2

Function is defined, if

(i) x(x+1)0, since domain of square root function.

(ii) x2+x+10, since domain of square root function.

(iii) x2+x+11, since domain of sin1 function.

From (ii) and (iii), 0x2+x+11x2+x0

0x2+x+11x2+x+11
x2+x+1=1
x2+x=0
x(x+1)=0
x=0,x=1


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