For the sine function : sin (x + 2pi) = sin x and sin (x + pi)= -sin x and for the cosine function , cos ( x + pi) = -cos x.
sin 2x sin x - cos x, for x = 7pi/6
=> sin 14pi/6 * sin 7pi/6 - cos 7pi/6
=> sin ( 2pi/6 + 2pi) * sin (pi/6 + pi) - cos( pi + pi/6)
=> - sin 2pi/6 * sin pi/6 + cos pi/6
Now sin 2pi/6 = .5 and cos pi/6 = sqrt 3/2
=> -(sqrt 3/ 2)(1/2) + sqrt 3/2
=> -sqrt 3 / 4 + 2*sqrt 3 / 4
=> sqrt 3 / 4
For x = 7pi/6, therefore sin 2x sin x - cos x = sqrt 3/ 4
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