If sin x = 3/10 then what is the value of tan x + cot x = ?

If sin x = $\frac{3}{10}$ then what is the value of tan x + cot x = ?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is Option 1 i.e. $\frac{100}{3\sqrt{91}}$ .

sin x = $\frac{3}{10}$ = P/H

By Pythagoras theorem

⇒ H² = B² + P²

⇒ 10² = B² + 3²

⇒ B² = 100 - 9

⇒ B² = 91

⇒ B = $\sqrt91$

The value of tan x + cot x = $3\over\sqrt91$ + $\sqrt91\over3$ = $(9 + 91)\over{3\sqrt91}$ = $100\over{3\sqrt91}$

SSC CGL 2023 PYQ — Question 72