Question

2) If tan x=3 cotx then x' is
A) 45°
В) 309
C) 60
DJ 90°​

Answer 1

Solution :-

tan x = 3cot x

⇒ tan x/cot x = 3

$\implies \rm \dfrac{tanx}{ \dfrac{1}{tanx} } = 3$

[ Because cot x = 1/cot x ]

$\implies \rm tanx \times tanx = 3$

⇒ tan² x = 3

⇒ tan x = √3

⇒ tan x = tan 60°

[ Because tan 60° = √3 ]

Comparing on both sides

⇒ x = 60°

Therefore the value of x is (C) 60°.

Answer 2

$\LARGE\underline\mathrm{Answer:}$

$\large{\sf{\underline{\underline \green{Given:-}}}}$

$\star$ $\normalsize\sf{Tanx \: = \: 3 cotx }$

$\large{\sf{\underline{\underline \green{To \: find:-}}}}$

$\star$ $\normalsize\sf{ Find \: the \: value \: of \: x }$

$\large{\sf{\underline{\underline \green{Step \: by \: step \: explanation:-}}}}$

➠$\large\sf{ \frac{Tanx}{Cotx} \: = \: 3}$

➠$\large\sf{ \frac{Tanx}{ \frac{1}{Tanx} } \: = \: 3}$

➠$\normalsize\sf{ Tan^2x \: =\: 3}$

➠$\normalsize\sf{Tan x \: = \: \sqrt{3} }$

➠$\normalsize\sf{ Tan x\: = \: Tan 60°}$

$\scriptsize\sf{\: \: \: \: \: (According \: of \: trigonometric \: ratios \:\red{Tan60° \: = \: \sqrt{3} })}$

➠${\boxed{\sf \purple{ Value \: of \: x \: is \: 60°}}}$