Let f(theta) = sin theta (sin theta + sin 3th | vedclass

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(C) Given $f(	heta) = \sin 	heta (\sin 	heta + \sin 3	heta)$.Using the identity $\sin 3	heta = 3\sin 	heta - 4\sin^3 	heta$,we have:$f(	heta)

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$ \ge 0$ for all real $	heta$

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(C) Given $f(	heta) = \sin 	heta (\sin 	heta + \sin 3	heta)$.Using the identity $\sin 3	heta = 3\sin 	heta - 4\sin^3 	heta$,we have:$f(	heta) = \sin 	heta (\sin 	heta + 3\sin 	heta - 4\sin^3 	heta)$$f(	heta) = \sin 	heta (4\sin 	heta - 4\sin^3 	heta)$$f(	heta) = 4\sin^2 	heta (1 - \sin^2 	heta)$Since $1 - \sin^2 	heta = \cos^2 	heta$,we get:$f(	heta) = 4\sin^2 	heta \cos^2 	heta$$f(	heta) = (2 \sin 	heta \cos 	heta)^2$$f(	heta) = (\sin 2	heta)^2$Since the square of any real number is always non-negative,$(\sin 2	heta)^2 \ge 0$ for all real $	heta$.Therefore,$f(	heta) \ge 0$ for all real $	heta$.

Let $f(\theta) = \sin \theta (\sin \theta + \sin 3\theta)$,then $f(\theta)$

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