Question

If cos x=-1/3 , x is in 3rd quadrant, find the value of sin(x/2) and cos(X/2).
class 11

Answer 1

Answer:

Step-by-step explanation:

Cosx=-1/3

Cosx=2cos^2(x)/2 -1

-1/3=2cos^2(x)/2 -1

1-1/3=2cos^2(x)/2

(3-1)/3=2cos^2(x)/2

2/3=2cos^2(x)/2

1/3=2cos^2(x)/2

1/6=cos^2(x)/2

Cosx/2=1/√6

Cos x=1-2sin^2(x)/2

-1/3=1-2sin^2(x)/2

1/3+1=2sin^2(x)/2

4/3=2sin^2(x)/2

Sinx/2=2/√6

Answer 2

Answer:

here ans is

Step-by-step explanation:

cosx=−31,π<x<23π

i.e. x lies in 3rd quadrant

Using 1−cosx=2sin22x⇒sin2x=±21−cosx

We get, sin2x=±21−(−31)=±64

As π<x<23π⇒2π<2x<43π and sin is positive in 2nd quadrant

∴sin2x=5

here you're answer mark as brainlist ✍