Question

Match the following:

Given sin x = $\frac{2}{5}$ and x $ϵ$ $(0,\frac{\Pi }{2})$

(p) cosx (1) $\frac{5}{2}$

(q) tanx (2) $\frac{\sqrt{21}}{2}$

(r) cosecx (3) $\frac{\sqrt{21}}{5}$

(4) $\frac{2}{\sqrt{21}}$

• 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

x is an acute angle (Given in the question) So we will construct appropriate right $△$ and find the ratios.

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

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

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

tanx = $\frac{2}{\sqrt{21}}$ $\left(\frac{Opposite}{Hypotenuse}\right)$

cosecx = $\frac{5}{2}$ $\left(\frac{Adjacent}{Hypotenuse}or\frac{1}{sinx}\right)$

So the answer is P-3, Q-4, R-1

Key steps: (1) Pythagoras's' theorem

(2) Calculating basic trigonometric ratios from a right-angled triangle.