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anonymous

  • one year ago

iif cosectheta-cottheta=1\2 then costheta=?

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  1. welshfella
    • one year ago
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    I'll use O for theta:- csc O - cot O = 1/2 what is cos O you might do it this way csc^2 O = 1 + cot^2 O so substituting ; sqrt( 1 + cot^2 O) + cot O = 1/2 solve for cot O then you can find cos O using other trig identities

  2. welshfella
    • one year ago
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    * typo in line 6 it should be sqrt( 1 + cot^2 O) - cot O = 1/2

  3. welshfella
    • one year ago
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    you can also find the value of angle O from cot O then find cos O

  4. welshfella
    • one year ago
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    I'll start the solution of the equation for you sqrt( 1 + cot^2 O) + cot O = 1/2 sqrt( 1 + cot^2 O) = cot O + 1/2 square both sides;- 1 + cot^2 O = cot^2 O + cot O + 1/4 now finding cot O is straightforward

  5. Loser66
    • one year ago
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    \(csc \theta =\dfrac{1}{sin\theta}\\cot \theta=\dfrac{cos\theta}{sin\theta}\) hence \(csc(\theta)-cot(\theta)= \dfrac{1}{sin(\theta)}-\dfrac{cos(\theta)}{sin(\theta)}=\dfrac{1-cos(\theta)}{sin(\theta)}=\dfrac{1}{2}\)

  6. Loser66
    • one year ago
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    Now, restrict the solution from 0, since if \(\theta =0\) , then \(sin(\theta )=0\), that make the expression undefined.

  7. Loser66
    • one year ago
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    we have: \(2(1-cos(\theta))= sin(\theta)\) square both sides and solve for \(cos (\theta)\)

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