How do you solve $(cot (x) + 1) (csc (x) - (\frac{1}{2}) = 0$ $(cot(x) + 1)(csc(x) - (1/2) = 0$ from [0,2pi]?

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How do you solve $(cot (x) + 1) (csc (x) - (\frac{1}{2}) = 0$ $(cot(x) + 1)(csc(x) - (1/2) = 0$ from [0,2pi]?

1 Answer

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Answer 1 · 2015-08-03T03:26:21

Solve: $(cot x + 1) (csc x - \frac{1}{2}) = 0$ $(cot x + 1)(cscx - 1/2) = 0$ $[0, 2 π]$ $[0, 2pi]$

Ans: $\frac{3 π}{4} and \frac{7 π}{4}$ $(3pi)/4 and (7pi)/4$

Explanation:

Make the 2 factors equal to zero.

(cot x + 1 = 0 --> cot x = -1 --> $x = \frac{3 π}{4}$ $x = (3pi)/4$ and $(7 \frac{π}{4})$ $(7pi/4)$
$\frac{1}{sin x} - \frac{1}{2} = 0$ $1/sin x - 1/2 = 0$ --> sin x = 2. Rejected because > 1

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How do you solve $(cot (x) + 1) (csc (x) - (\frac{1}{2}) = 0$ $(cot(x) + 1)(csc(x) - (1/2) = 0$ from [0,2pi]?

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How do you solve $(cot (x) + 1) (csc (x) - (\frac{1}{2}) = 0$ $(cot(x) + 1)(csc(x) - (1/2) = 0$ from [0,2pi]?