Question

Which expression is equivalent to ½ sin 2 theta for all values of theta

Answer 1

Given:

Given the expression

`(1)/(2)\sin2\theta`

Required: An equivalent expression

Step-by-step explanation:

Use the formula

`\sin2\theta=2\sin\theta\cos\theta`

Dividing by 2 on both sides gives

`\begin{gathered} (1)/(2)\sin2\theta=(1)/(2)(2\sin\theta\cos\theta) \\ =\sin\theta\cos\theta \end{gathered}`

Option D is correct.

Final Answer: An equivalent expression of

`(1)/(2)\sin2\theta`

is

`\cos\theta\sin\theta`