- Home
- Standard 11
- Mathematics
Trigonometrical Equations
easy
The expression $(1 + \tan x + {\tan ^2}x)$ $(1 - \cot x + {\cot ^2}x)$ has the positive values for $x$, given by
A
$0 \le x \le \frac{\pi }{2}$
B
$0 \le x \le \pi $
C
For all $x \in R$
D
$x \ge 0$
Solution
(c) The expression is $\frac{{(1 + \tan x + {{\tan }^2}x)(1 + {{\tan }^2}x – \tan x)}}{{{{\tan }^2}x}}$
$= \frac{{{{(1 + {{\tan }^2}x)}^2} – {{\tan }^2}x}}{{{{\tan }^2}x}}$
Obviously, $1 + {\tan ^2}x \ge {\tan ^2}x,{\rm{ }}\forall {\rm{ }}x$.
Hence it is positive for all value of $x.$
Standard 11
Mathematics
