Question

How do you show that `2 \sin x \cos x = \sin 2x`? is true for `(5pi)/6`?

Answer 1

To prove it, evaluate the left-hand side and the right-hand side separately and show that they are the same.

(LHS)`=2sin({5pi}/6)cos({5pi}/6)=2cdot1/2cdot(-sqrt{3}/2)=-sqrt{3}/2`

(RHS)`=sin(2cdot{5pi}/6)=sin({5pi}/3)=-sqrt{3}/2`

Hence, (LHS)`=`(RHS) for `x={5pi}/6`.

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I hope that this was helpful.