Mathematics

Mathematics

Problem

Consider the expression S(θ)=sin⁡(90∘−θ)sin⁡θ+cos⁡(90∘−θ)cos⁡θS(\theta) = \sin(90^\circ - \theta)\sin \theta + \cos(90^\circ - \theta)\cos \theta. a. (i) Show that S(θ)=sin⁡2θS(\theta) = \sin 2\theta for every acute angle θ\theta. b. (ii) Using the result from part (i), evaluate sin⁡(90∘−35∘)sin⁡35∘+cos⁡(90∘−35∘)cos⁡35∘\sin(90^\circ - 35^\circ)\sin 35^\circ + \cos(90^\circ - 35^\circ)\cos 35^\circ.

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