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November 15th, 2016, 09:34 AM   #1
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Trigonometric identities

Can anyone please help me with this question?

Solve the following between the angles of 0 and 360 deg
4cot²x - 6 cosec x = -6

Last edited by skipjack; November 16th, 2016 at 06:35 AM.
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November 15th, 2016, 10:25 AM   #2
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note the identity ...

$\cot^2{x} = \csc^2{x} - 1$

substitute $\csc^2{x} - 1$ for $\cot^2{x}$ and solve the resulting quadratic ...
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November 16th, 2016, 05:51 AM   #3
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Can you show me the first stages of substituting the identity? I understand how to solve the quadratic and also getting the angles between 0 and 360, but I do not understand how to substitute the identity.

Last edited by skipjack; November 17th, 2016 at 05:56 AM.
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November 16th, 2016, 06:07 AM   #4
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$4\cot^2{x}-6\csc{x}=-6$

substitute ...

$4(\csc^2{x}-1)-6\csc{x}=-6$

now, proceed ...
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November 24th, 2016, 12:21 PM   #5
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Roots of the equation are cosec x = 1/2 & cosec x = 1
Therefore sin x = 2 & sin x =1
sin x = 2: no solution, because sin x belongs to [-1, 1]
sin x = 1 => x = n*PI + (-1)power of n * PI/2 for all values on n belongs to Z
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November 24th, 2016, 09:17 PM   #6
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It's simpler to state that sin x = 1 implies x = $\pi$/2 + 2n$\pi$, where n is an integer.
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