Question

cos X =-1/2 , X lies in third quadrant
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Answer 1

Answer:

cos x -1/2 x lies in the third quadrant

Step-by-step explanation:

Answer 2

AnsWer :

tan x = √3.

To FinD :

The value of tan x.

SolutioN :

$\tt Cos\, x = -\dfrac{1}{2} \: , x \: lies \: in \: third \: Quadrant.$

We know, that.

• Sin²A + Cos²A = 1.

$\tt \longmapsto {sin}^{2} x + {cos}^{2} x= 1.$

$\tt \longmapsto {sin}^{2} x + { \bigg(\dfrac{1}{2} \bigg) }^{2} = 1.$

$\tt \longmapsto {sin}^{2} x = 1 - \dfrac{1}{4}$

$\tt \longmapsto {sin}^{2} x = \dfrac{4 - 1}{4}$

$\tt \longmapsto {sin}^{2} x = \dfrac{3}{4}$

$\tt \longmapsto {sin} x = \pm \dfrac{ \sqrt{3} }{2}$

★ Now, given x lies on Quadrant third, so

• Sin x = - √3 / 2.
• Cos x = - 1 / 2.

★ Now, Let's Find the Tan x = ?

$\tt \longmapsto \dfrac{Sin x }{Cos x } = tan x$

$\tt \longmapsto \dfrac{-\frac{\sqrt{3}}{2}}{- \frac{1}{2}} = tan x$

$\tt \longmapsto tan \,x =\sqrt{ 3}.$

Therefore, the value of tan x is √3.