Question

Suppose that $\theta$ is a number and 0 < $\theta$ < 90${}^{\circ }$. Consider the following statements and select the correct choice:

I : sec (${\theta }^{\circ }$) < 1 ;

II : sec (${\theta }^{\circ }$) $=$ 1 ;

III : sec (${\theta }^{\circ }$) > 1 ;

• A. Only I is possible
• B. All are possible
• C. Only III is possible
• D. Only I is impossible

Answer 1

The correct option is C Only III is possible

As the value of $\sec \theta$ is always greater than one for $0°<\theta <90°.$

$\sec 0^0=1,\sec {30}^0=\frac{2}{\sqrt{3}},\sec {45}^0=\sqrt{2},\sec {60}^0=2,\sec {90}^0=\infty ,$

Hence one III statement is possible i.e,

$\sec \left(\theta \right)>1.$

Hence, the answer is an option C.