Question

Sin theta = x+( 1/x) is possible or impossible for any real x ??

Answer 1

sin∅ = x + 1/x isn't possible ,

reason:- we know, that sin∅ lies between -1 to 1. and sin²∅ lies between 0 to 1 .

here, sin∅ = x + 1/x
take square both sides,
sin²∅ = x² + 1/x² + 2.x.1/x
sin²∅ = x² + 1/x² +2
here we can see that RHS is always greater then 2 , but maximum value of sin²∅ is 1 .
hence,
sin²∅ ≠ x² + 1/x² +2
hence, sin∅ ≠ x + 1/x for all x real numbers

Answer 2

Answer: It is possible and impossible

Step-by-step explanation: sinФ = x + (1/x)

Let x be +2

then, x + (1/x) becomes 2 + (1/2)

= 2 + 0.5  (1/2 is nothing but 0.5)

= 2.5 which is impossible.

Let x be -2

∴ x + (1/x) = -2 + (1/-2)

-2 and -2 cancelled

Answer is 1 which is possible

(this answer is from my teacher)