The expression $\left( 1 + an x + an^{2}x ight)(1 - \cot x + \cot^{2}x)$ has the positive values for $x$, given by

Question

The expression $\left( 1 + 	an x + 	an^{2}x ight)(1 - \cot x + \cot^{2}x)$ has the positive values for $x$, given by

Dr. Abubacker · Accepted Answer

(c)
$\left( 1 + 	an{x + 	an^{2}x} ight)(1 - \cot{x + \cot^{2}x})$
$= \frac{\left( 1 + 	an{x + 	an^{2}x} ight)(1 + 	an^{2}{x - 	an x})}{	an^{2}x}$
$= \frac{\left( 1 + 	an^{2}x ight)^{2} - 	an^{2}x}{	an^{2}x}$
Obviously, $1 + 	an^{2}{x \geq 	an^{2}{x,\ \forall\ x \in R}}$

Q. The expression $\left( 1 + \tan x + \tan^{2}x \right)(1 - \cot x + \cot^{2}x)$ has the positive values for $x$, given by

Explanation

Reviewed by Dr. Abubacker

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