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Prove that $\sin{(45^{\circ} + \theta)}.\sin{(45^{\circ} - \theta)} = \frac{1}{2}\cos{2\theta}$. Hence determine the value of $\sin{75^{\circ}}.\sin{15^{\circ}}$
in Mathematics by Bronze Status (8,142 points) | 68 views

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use compound angle identity

sin75.sin15=sin(45+30).sin(45-30)= 1/2 .cos2.30

                                                     = 1/2 .cos 60  use special angle value for cos60

                                                     = 1/2 x 1/2 = 1/4
by Diamond (43,720 points)

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