Question

Sum of all possible values of x satisfying the equation 4cosx/2 + since.sinx/2 = 0, where x belongs to [0,315], is equal to?

Answer 1

Perhaps there is a mistake in typing the question. I will correct it as follows.

4 Cos x/2 + sin x/2 = 0, x € [0, 315].
Then x/2 € [0, 157.5].

Given Tan x/2 = -1/4.
x/2 = 165.964° or 345.964°.

So there is no solution for x in the given range.
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If the question is:
4 cos x/2 + sin x × sin x/2 = 0.

4 cos x/2 + 2 sin x/2 * cos x/2 * sin x/2 = 0.

Either Cos x/2 = 0 , ie. x = 180°
OR, 4 + sin^2 x/2 = 0. But this is not possible.

So only one answer: x = 180°.