Prove that `sin^2theta

Explanation

we have to prove that `sin^(2)theta lt theta "an" (sin theta)`
or `sin("sin theta")/("sin" theta)gt("sin" theta)/(theta)`
or `f("sin" theta)gtf(theta)` where `f(x) =(sinx)/(x)`
Now `f(x) =(xcos x-sinx)/(x^(2))`
`=(cosx(x-tanx))/(x^(2))lt0(as x lt tan x for x in (0,pi//2))`
`therefore` f(x) is decreasing function
Also we know that `sin theta lt theta for 0 lt theta (pi)/(2)`
`f(sin theta)gtf(theta)`
`sin(sin theta)/(sin theta)gt(sin theta)/(theta)`
`sin^(2)theta lt theta sin(sin theta)for 0 lt theta lt(pi)/(2)`