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simplify cosec(delta)[cos (delta) -1] by expressing it in terms of (tan (delta/2))

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bubbletrea | Student, Grade 11 | Honors

Posted July 13, 2013 at 11:35 AM via web

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simplify cosec(delta)[cos (delta) -1] by expressing it in

terms of (tan (delta/2))

Tagged with math, maths, trigonometry

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aruv | High School Teacher | Valedictorian

Posted July 13, 2013 at 11:47 AM (Answer #1)

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`cos(delta)=1-2sin^2(delta/2)`

`cosec(delta)=1/sin(delta)=1/(2sin(delta/2)cos(delta/2))`

Thus

`cosec(delta){cos(delta)-1}=(1/(2sin(delta/2)cos(delta/2)))(-2sin^2(delta/2))`

`` cancel out the terms common in numerator and denominator

=`(-sin(delta/2))/cos(delta/2)`

`=-tan(delta/2)`

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