Posted by **Steve** on Thursday, December 17, 2009 at 9:27pm.

Find all solutions of the equation: cot x sec x = 2 cot x.

A) x = 2ð/3 + nð or x = 4ð/3 + nð or 0 + nð

B) x = 2ð/3 + 2nð or x = 4ð/3 + 2nð or 0 + nð

C) x = ð/3 + 2nð or x = 5ð/3 + 2nð or 0 + nð

D) x = ð/3 + nð or x = 5ð/3 + nð or 0 + nð

- trig -
**Reiny**, Thursday, December 17, 2009 at 10:28pm
cot x sec x = 2 cot x.

cotx secx - 2cot x = 0

cotx(secx - 2)

cotx = 0 or secx = 2

if cotx = 0

the cotangent is zero when the tangent is undefined, and the tangent is undefined at 90º (pi/2) and 270º (3pi/2)

or

cosx/sinx = 0

cosx = 0 , x = pi/2 or 3pi/2

if secx = 2

cosx = 1/2, x = pi/3 or 5pi/3

add n(2pi), where n is an integer, to get the general solutions.

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