Answer :

Answer: [tex]\frac{1}{2}sin2θ\text{ = cos\theta sin\theta \lparen option D\rparen}[/tex]

Explanation:[tex]\begin{gathered} Given: \\ \frac{1}{2}sin2\theta \\ \\ We\text{ want to find the equivalent of the above for all values of \theta} \end{gathered}[/tex]

To solve this, we need to find the trigonometry identity for sin2θ:

[tex]sin2θ\text{ = 2sin\theta cos\theta}[/tex]

substitute the expression for sin2θ into the given trigonometry:

[tex]\begin{gathered} \frac{1}{2}sin2θ\text{ = }\frac{1}{2}(2sinθcosθ) \\ \\ \frac{1}{2}sin2θ\text{ = sin\theta cos \theta} \\ \\ Hence,\text{ the equivalence of }\frac{1}{2}sin2θ\text{ = cos\theta sin\theta \lparen option D\rparen} \end{gathered}[/tex]

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