Simplify (1+cos(x/2)-sin(x/2))/(1-cos(x/2)-s in(x/2))

Recall the double angle identities:

cos(x/2) = cos(x/4 + x/4) = cos²(x/4) - sin²(x/4)

sin(x/2) = sin(x/4 + x/4) = 2 sin(x/4) cos(x/4)

So

(1 + cos(x/2) - sin(x/2)) / (1 - cos(x/2) - sin(x/2))

= (1 + cos²(x/4) - sin²(x/4) - 2 sin(x/4) cos(x/4)) / (1 - cos²(x/4) + sin²(x/4) - 2 sin(x/4) cos(x/4))

sin²(x) + cos²(x) = 1, so

(1 + cos(x/2) - sin(x/2)) / (1 - cos(x/2) - sin(x/2))

= (2 cos²(x/4) - 2 sin(x/4) cos(x/4)) / (2 sin²(x/4) - 2 sin(x/4) cos(x/4))

= (cos(x/4) / sin(x/4)) • (2 cos(x/4) - 2 sin(x/4)) / (2 sin(x/4) - 2 cos(x/4))

=  (cos(x/4) / sin(x/4)) • (-1)

= - cot(x/4)

it is definatly the 3rd one. very much looks like it, for a good chance, the third one would be best for you.

8(4)^8=72^feet to say that the total can conclude to 8(4) which as you know would mean 8 x 4. that equals 32w. 32^ could make a 72 answer as well. but your coefficent will remain w so your answer is 72w.

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