Question

Match the following:

Given $\sin x$ = $\left(\frac{2}{5}\right)$ and $x\in (0,\frac{\pi }{2})$

$\begin{array}{cc}\text{(p)}\cos x& \text{(1)}\frac{5}{2}\\ \text{(q)}\tan x& \text{(2)}\frac{\sqrt{21}}{2}\\ \text{(r)}\csc x& \text{(3)}\frac{\sqrt{21}}{5}\\ & \text{(4)}\frac{2}{\sqrt{21}}\end{array}$

• A. P-2, Q-3, R-4
• B. P-3, Q-2, R-4
• C. P-2, Q-3, R-1
• D. None of these

Answer 1

The correct option is D

None of these

As $x$ is an acute angle,

We will construct the triangle in such a way that $\sin x$ = $\frac{2}{5}$ (Above figure).

Using Pythagoras theorem, we can find the $3^{rd}$ side of the $△$.
So the triangle will be

Now, $\cos x$ = $\frac{\sqrt{21}}{5}$ $\left(\frac{Adjacent}{Hypotenuse}\right)$

$\tan x$ = $\frac{2}{\sqrt{21}}$ $\left(\frac{Opposite}{Adjacent}\right)$

$\csc x$ = $\frac{5}{2}$ $\left(\frac{Hypotenuse}{Opposite}or\frac{1}{sinx}\right)$

So the answer is $p-3,q-4,r-1$