2013-II-23

Ans: B
I must be true.

$\begin{array}{rcl}
\text{LHS} & = & \tan x \tan (90^\circ – x ) \\
& = & \tan x \times \dfrac{1}{\tan x} \\
& = & 1 \\
& = & \text{RHS}
\end{array}$

II may be false. Take $x=45^\circ$.

$\begin{array}{rcl}
\text{LHS} & = & \sin 45^\circ – \sin (90^\circ-45^\circ) \\
& = & 0 \\
& \not < & 0 \end{array}$

III must be true.

$\begin{array}{rcl}
\text{LHS} & = & \cos x +\cos (90^\circ – x) \\
& = & \cos x + \sin x \\
& > & 0 \\
& = & \text{RHS}
\end{array}$