Number of solutions of equation `sin(cos^(-1)(tan(sec^(-1)x)))=sqrt(1+x)` is/are ____

Answer

0

Explanation

Now, `sin (cos^(-1) (tan (sec^(-1) x)))`
`= sin (cos^(-1) (tan (tan^(-1) sqrt(x^(2) -1)))`
`= sin (cos^(-1) (sqrt(x^(2) -1)))`
`= sin (sin^(-1) (sqrt(2 -x^(2))))`
`= sqrt(2 -x^(2))`
For `x in [-sqrt2, -1] uu [1, sqrt2] and x ge -1`, we have
`2 -x^(2) = 1 + x`
`:. x^(2) + x - 1 = 0`
`x = (-1 +- sqrt5)/(2) = 0.615, -1.615`
None of which satisfies the condition `x in [-sqrt2, -1] uu [1, sqrt2]`