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

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Answer 1 · 2014-10-24T00:56:20

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 $x={5pi}/6$ .

I hope that this was helpful.

How do you show that 2 \sin x \cos x = \sin 2x2 \sin x \cos x = \sin 2x? is true for (5pi)/6(5pi)/6?