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Solve $\cos 3\theta\,.\,\cos\theta-\sin 3\theta\,.\,\sin\theta=-\frac{1}{2}$
in Grade 12 Maths by Bronze Status (5.9k points) | 14 views

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apply compound angle identity

cos(3x +x) = -1/2

  cos(4x) = -1/2

           4x = 60 degrees

cos is negative in 2nd and 3rd quadrants:

  2nd=  4x= 180-60 = 120

                   4x= 120

                      x= 30

3rd= 4x= 180+60

           4x= 240

           x= 60

hence x= 30 and 60 degrees.
by Diamond (82.9k points)

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