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Question #184d3

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Oct 10, 2016

$csc (2 x) = \frac{1}{2 sin (x) cos (x)} = \frac{1}{2} csc (x) sec (x)$ $csc(2x)= 1/(2sin(x)cos(x))=1/2csc(x)sec(x)$

Explanation:

Given the double angle identity for the sine function, this is just a matter of applying that the cosecant function is just the reciprocal of sine.

$csc (2 x) = \frac{1}{sin (2 x)}$ $csc(2x) = 1/sin(2x)$

$= \frac{1}{2 sin (x) cos (x)}$ $= 1/(2sin(x)cos(x)$

$= \frac{1}{2} \cdot \frac{1}{sin (x)} \cdot \frac{1}{cos (x)}$ $=1/2*1/sin(x)*1/cos(x)$

$= \frac{1}{2} csc (x) sec (x)$ $=1/2csc(x)sec(x)$

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