Question

a+c=2b then sina-sinc/cosa-cosc

Answer 1

Answer:

-cot(b)

Step-by-step explanation:

Hi,

Given a + c = 2b

To simplify sina-sinc/cosa-cosc

Using half-angle formulae, sina - sinc = 2sin(a-c)/2cos(a+c)/2

cosa - cosc = -2sin(a-c)/2sin(a+c)/2

So, sina-sinc/cosa-cosc

= [2sin(a-c)/2cos(a+c)/2]/[2sin(a-c)/2sin(a+c)/2]

= - cot(a+c)/2

Using a + c = 2b

we get (a + c)/2 = b,

Hence ,

sina-sinc/cosa-cosc = - cot(b).

Hope, it helps !