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Simplify $\sin(4x)\cos(4x)$ using double angle or compound trigonometry.

Can someone please show me how its done, Ive tried several times but no where near the answer.

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    $\begingroup$ What do you mean by "solve"? What is there to solve? $\endgroup$ – Pedro Tamaroff Jul 10 '13 at 4:49
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    $\begingroup$ As stated there is nothing to solve here. Do you mean $\sin(4x) \cos(4x) = 0$? $\endgroup$ – Joel Jul 10 '13 at 4:50
  • $\begingroup$ Simplify, sorry. $\endgroup$ – Red Queen10101 Jul 10 '13 at 4:51
  • $\begingroup$ @RedQueen10101 is it what i have answered or you mean different one? $\endgroup$ – dato datuashvili Jul 10 '13 at 4:56
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    $\begingroup$ represent $8*x=2*(4*x)$ $\endgroup$ – dato datuashvili Jul 10 '13 at 4:59
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The double angle formula is $ \ 2 \sin\theta\cos\theta = \sin(2\theta) \iff \sin\theta\cos\theta = \frac{1}{2} \sin(2\theta)$.

By applying this formula with $\theta = 2x$, we obtain

$$\sin4x\cos4x=\frac{1}{2} \sin(8x).$$

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$\sin4x\cos4x$ using identiity that $\sin(2\theta)=2\sin\theta\cos\theta$,we get

$\sin4x\cos4x=\frac{\sin(8x)}{2}$

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    $\begingroup$ I'm reasonably sure the question is asking to simplify in terms of $\sin(x)$ and $\cos(x)$. $\endgroup$ – Zev Chonoles Jul 10 '13 at 4:54
  • $\begingroup$ Also, named math operators should appear upright, and the common ones have their own code for this purpose (e.g. \sin, \log - see entry 11 in our MathJax guide). $\endgroup$ – Zev Chonoles Jul 10 '13 at 4:54
  • $\begingroup$ ok i was thinking that he wanted like this,then it is his rights to ask it more clearly,what does mean simplify in terms of sin and cosine?by which way?i did not understand $\endgroup$ – dato datuashvili Jul 10 '13 at 4:55
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    $\begingroup$ In textbooks, sometimes “simplify” means “complicate”. I like this answer fine. $\endgroup$ – Lubin Jul 10 '13 at 4:59
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    $\begingroup$ I feel like Dato has the right of it. This is set up as a clear application of the double angle formula as you would find it in the exercises of a textbook. $\endgroup$ – Joel Jul 10 '13 at 5:01

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