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Jatin Parmar · Answer 1 · 2023-01-15T13:41:02+0000

Answer:
$(1)/(2)sin2θ\text{ = cos\theta sin\theta \lparen option D\rparen}$

Step-by-step explanation:
$\begin{gathered} Given: \\ (1)/(2)sin2\theta \\ \\ We\text{ want to find the equivalent of the above for all values of \theta} \end{gathered}$

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

$sin2θ\text{ = 2sin\theta cos\theta}$

substitute the expression for sin2θ into the given trigonometry:

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

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