Verify the identity cos x cos ysin x sin y tan x y2 Sta

Verify the identity. cos x - cos y/sin x - sin y = - tan x + y/2 Start with the numerator of the left side and apply the appropriate formula of sum-to-product cos x - cos y = Now use the sum-to-product formula on the denominator of the left side. sin x - sin y = In the numerator and denominator, substitute the expressions found in previous steps. Then divide out the common factor of the expression. = (simplify your answer.) The fraction from the previous step then simplifies to - tan x + y/2 using what? Even-Odd Identity Pythagorean Identity Quotient Identity Reciprocal Identity

Solution

(cos x-cos y)/(sinx -siny)=-tan((x+y)/2)

cos x- cos y= -2 sin((x+y)/2)sin((x-y)/2)

We have to write that in the first fill in the blanks

sin x - sin y=2(sin(x+y)/2)sin((x-y)/2)

And that we have to write in second fill in the blanks

substituting the values of cos x - cos y and sin x - sin y

-2(sin(x+y)/2)sin((x-y/2))/2 cos ((x+y)/2)sin((x-y)/2)

And that we have to write in third fill in the blanks

- sin((x+y)/2)/cos((x+y)/2)

-tan ((x+y)/2)

Quotient identity is tan x= sinx/ cos x

And in the last step we use this identity

Therefore the correct option is quotient identity.