Question #01a4e

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Question #01a4e

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Answer 1 · 2017-03-01T04:32:04

Rearrange and solve

Explanation:

${csc}^{2} (\frac{x}{2}) = 2 sec x$ $csc^2(x/2) = 2secx$
$\frac{1}{{sin}^{2} (\frac{x}{2})} = \frac{2}{cos x}$ $1/(sin^2(x/2)) = 2/cosx$
$cos x = 2 {sin}^{2} (\frac{x}{2})$ $cosx = 2sin^2(x/2)$
$1 - 2 {sin}^{2} (\frac{x}{2}) = 2 {sin}^{2} (\frac{x}{2})$ $1-2sin^2(x/2) = 2sin^2(x/2)$
${sin}^{2} (\frac{x}{2}) = \frac{1}{4}$ $sin^2(x/2) = 1/4$
$sin (\frac{x}{2}) = \pm \frac{1}{2}$ $sin(x/2) = \pm 1/2$
$\frac{x}{2} = \frac{π}{6} + k π, \frac{5 π}{6} + k π$ $x/2 = pi/6 + kpi,(5pi)/6+kpi$
$x = \frac{π}{3} + 2 k π, \frac{5 π}{3} + 2 k π$ $x = pi/3+2kpi,(5pi)/3+2kpi$

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Question #01a4e

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