sin inverse pf 1+xsquare /2x+square root of cos of sinx
Answer (1)
29th Nov, 2020
Hello,
Is your question sin^-1((1+x^2)/2x)) + sqrt((cos(sin x))?
Assuming it is then-
To define the value of x for it-
Then we know that value of sqrt((cos(sin x)) will always come as positive.
But (1+x^2)/2x) value should lie between 1 and -1 because of sin-ie
-1 <= (1+x^2)/2x) <= 1
Solving -1 < (1+x^2)/2x)
Hence x^2+1 >= -2x
= (x+1)^2 >= 0 ------(1)
Hence the value of this quantity will also be a positive R value always.
Now solving (1+x^2)/2x) <= 1 similarly we get
(x-1)^2 <= 0 ------(2)
Conditions (1),(2) will be true only at x= 1,-1
Hence in this domain x belongs to only 1 and -1;
x belongs to { 1,-1}
Hope this helps.
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