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Trigonometric-Equations

Probability Introduction :

Solve the following  for \(0\leq \Theta < 2\pi \)

Q1) \(2\sin ^{2}\Theta -\sin \Theta -1= 0\)

Solution:

    \(2\sin ^{2}\Theta -\sin \Theta -1= 0\)

    \(2\sin ^{2}\Theta -2\sin \Theta +\sin \Theta -1=0\)
    \(\left ( \sin \Theta -1 \right )\left ( 2\sin \Theta +1 \right )= 0\)
    \(\sin \Theta -1= 0\) or \(2\sin \Theta +1= 0\)

      \(\sin \Theta = 1\) or \(\sin \Theta = \frac{-1}{2}\)

       \(\Theta =\frac{\pi }{2},\frac{7\pi }{6},\frac{11\pi }{6}\)

   

   Q2) \(\left ( \cot \Theta +1 \right )\left ( \csc \Theta -1/2 \right )= 0\)

Q3) \(\left ( \tan \Theta -1 \right )\left ( \sec \Theta -1 \right )= 0\)

Q4)\(\cos \left ( 4\Theta  \right )-\cos \left ( 6\Theta  \right )=0\)

Q5)\(12\cos ^{2}\Theta =9\)
Q6)\(\cos \left ( 2\Theta  \right )+10\sin ^{2}\Theta =5\)

Q7)\(\sin ^{2}\Theta =7\left ( \cos \Theta -1 \right )\)

Q8)


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