SOLUTION: show that {{{(sin(x)sin(2x)+sin(3x)sin(6x))/(sin(x)cos(2x)+sin(3x)cos(6x))=tan(5x)}}}

Question 883546: show that
Answer by cigany29(23) (Show Source): You can put this solution on YOUR website!

Let's break it down first by applying our product-to-sum formulae!
� ==
� ==
�==
�==
Remember:
* cos(-x)=cos(x)
*sin(-x)=-sin(x)
SO:
�=
�=
�=
�=
Now lets put it together!

That looks kinda messy, so lets simplify that again and while we're at it, we'll get rid of one division by multiplying by the reciprocal!

*
Cancel the 2's and we're left with:

Now we're going to apply the sum-to-product formulae!
�== Again, sin(-x)=-sin(x) so it's = to
�==
Now we'll put the whole thing together:
=
which simplifies to:
=
and at last we have

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