Question

show that the equation sin theta =x plus 1 by x is impossible if x is real ​

Answer 1

we know that,

$arithmetic \: mean \geqslant geometric \: mean \\ therefore \\ \frac{x + \frac{1}{x} }{2} \geqslant {(x \times \frac{1}{x} )}^{ \frac{1}{2} } \\ x + \frac{1}{x} \geqslant 2 \\ i.e. \: minimum \: value \: of \: x + \frac{1}{x} \: is \: 2 \\ while \: maximum \: value \: of \: \sin( \theta ) = 1 < 2$

hence sin(\theta) ≠ x+(1/x), for any x€ R