# Equality of trigonometry function.

I can't seem to figure this out. Is sin 2x = 2sin x ? I know this might be a silly question but I don't know.

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Please try and use titles which reflect the mathematical content of the question. –  Asaf Karagila Oct 11 '12 at 15:55
What if $x=\pi/2$? –  David Mitra Oct 11 '12 at 15:56
figured it out thank you for you help :) –  Cioroianu Denis Oct 11 '12 at 15:58
$\sin 2x \neq 2 \sin x$. Look up "double angle identities" –  The Chaz 2.0 Oct 11 '12 at 15:58

No.

For example (using David Mitra's example of $x=\frac{\pi}{2}$): $$\sin\left(2 \times \frac{\pi}{2}\right) = \sin\left({\pi}\right) = 0$$ while $$2 \times \sin\left(\frac{\pi}{2}\right) = 2 \times \sin\left(\frac{\pi}{2}\right) = 2.$$

A correct expression would be $$\sin\left(2 x\right) = 2 \sin(x) \cos(x).$$

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The most obvious way to check the validity of a given trigonometric identity is to plug in specific values on both sides of the identity. For example, if you plug in $\dfrac{\pi}{2}$ on both sides of the given identity, you get $0$ on the LHS and $2$ on the RHS.

Observe also that the absolute maximum value of $\sin(2x)$ is $1$, whereas the absolute maximum value of $2 \sin(x)$ is $2$.

Furthermore, the period of $\sin(2x)$ is $\pi$, whereas the period of $2 \sin(x)$ is $2 \pi$.

All these indicate that the given trigonometric identity is not valid. The correct identity, of course, is $\sin(2x) = 2 \sin(x) \cos(x)$.

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No. $\sin(2x)=2\sin x\cos x$. Not that friendly with addition and multiplication..

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