Question

sina-sinb=1/3 and cosb-cosa=1/2 then cot(a+b/2)=

Answer 1

Hi friend!!

Given, sina-sinb=1/3

→ 2cos(a+b/2)sin(a-b/2)=1/3 -------------(1)

Given, cosb-cosa=1/2

→-2sin(b+a/2)sin(b-a/2)=1/2

→2sin(b+a/2)sin(a-b/2)=1/2 --------------(2)

(1)/(2) gives..

cot(a+b/2)=(1/3)×2

=2/3

I hope this will help u ;)

Answer 2

Answer:

2/3.

Step-by-step explanation:

Given,

Sina-Sinb=1/3

→ 2cos(a+b/2)sin(a-b/2)=1/3 -------------(1)

Given, cosb-cosa=1/2

→-2sin(b+a/2)sin(b-a/2)=1/2

→2sin(b+a/2)sin(a-b/2)=1/2 --------------(2)

Now,

Dividing equations 1 and 2, we get

To Find,

cot(a+b/2)

=(1/3)×2

=2/3

Hence, the answer is 2/3.

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