sin θ = (1/2) (√(x/y) + √(y/x)) necessarily implies :

Question

sin θ = (1/2) (√(x/y) + √(y/x)) necessarily implies : (A) x > y (B) x < y (C) x = y (D) both x and y are purely imaginary

Tardigrade Admin · Accepted Answer

Put t = √(x/y) > 0, Consider t+(1/t) = (√t - (1/√t))2 + 2 ge 2 equality holding iff t = 1 Also, t+(1/t) = 2 sin θ le 2, so that t should necessarily be 1, i.e., x = y.

Q. $s in θ = \frac{1}{2} (\frac{x}{y} + \frac{y}{x})$ necessarily implies :

x > y

x < y

x = y

both x and y are purely imaginary

Put $t = \frac{x}{y} > 0,$
Consider $t + \frac{1}{t} = (t - \frac{1}{t})^{2} + 2 \geq 2$ equality holding
iff $t = 1$
Also, $t + \frac{1}{t} = 2 s in θ \leq 2$ , so that t should necessarily
be 1, i.e., $x = y .$

Q. sinθ=21​(yx​​+xy​​) necessarily implies :