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freckles
 one year ago
Made a calculus question for fun. \[\int\frac{5 \cos(x)2 \sin(x)}{ 5 \sin(x)2 \cos(x)} dx\]
freckles
 one year ago
Made a calculus question for fun. \[\int\frac{5 \cos(x)2 \sin(x)}{ 5 \sin(x)2 \cos(x)} dx\]

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freckles
 one year ago
Best ResponseYou've already chosen the best response.1By the way I'm not sure if my way is the hard way or not but I like it and I think it is fun.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2I'm starting with \[a\cos x +b\sin x= C\cos(x +\phi)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 can you help me with a question please :)

freckles
 one year ago
Best ResponseYou've already chosen the best response.1err that is my way @ganeshie8 :p

freckles
 one year ago
Best ResponseYou've already chosen the best response.1So problem is too easy. :p

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0someone please help :(

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 ? @freckles ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1You could mention your question in chat @geny55 .

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is moisture supply abiotic or biotic?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1Well this isn't really chat... but okay.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1You might mention your question though in chat by posting a link to your question .

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{5 \cos(x)2 \sin(x)}{ 5 \sin(x)2 \cos(x)} =\dfrac{\cos(x  \arctan(2/5))}{ \cos(x\arctan(5/2))}\] ?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2idk readily what to next..

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 is moisture supply abiotic or biotic?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{\cos(a+x)}{\cos(b+x)} =\frac{\cos(x+b+(ab))}{\cos(b+x)}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1use sum identity on top

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Wow! that simplifies nicely !

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Let \(a = \arctan(2/5)\) and \(b = \arctan(5/2)\) \[\begin{align} &\frac{5 \cos(x)2 \sin(x)}{ 5 \sin(x)2 \cos(x)}\\~\\ & =\dfrac{\cos(x a)}{\cos(xb)}\\~\\ & =\dfrac{\cos((x b)+(ba))}{\cos(xb)}\\~\\ &=\cos(ba)  \sin(ba)\tan(xb) \end{align}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\int\limits \frac{ a \cos(x)+b \sin(x)}{c \cos(x)+d \sin(x)} dx \\ \frac{\sqrt{a^2+b^2}}{\sqrt{c^2+d^2}}\int\limits \frac{\cos(x+A)}{\cos(x+B)} dx \\ \sqrt{\frac{a^2+b^2}{c^2+d^2}} \int\limits \frac{\cos(x+B+(AB)}{\cos(x+B)} dx \\ \sqrt{\frac{a^2+b^2}{c^2+d^2}} \int\limits \frac{\cos(x+B) \cos(AB) \sin(x+B)\sin(AB)}{\cos(x+B)} dx \\ \sqrt{\frac{a^2+b^2}{c^2+d^2}} ( \int\limits \cos(AB) dx\sin(AB) \int\limits \tan(x+B) dx) \\ \sqrt{\frac{a^2+b^2}{c^2+d^2} } (\cos(AB)x+\sin(AB) \ln\cos(x+B)) +K\] if I didn't make a mistake we can do a more general form in this way

freckles
 one year ago
Best ResponseYou've already chosen the best response.1\[\sqrt{ \frac{a^2+b^2}{c^2+d^2}} \cos(AB) x+\sqrt{\frac{a^2+b^2}{c^2+d^2}}\sin(AB) \ln\cos(x+B)+K \\ \text{ where } A=\arctan(\frac{b}{a}) \text{ and } B=\arctan(\frac{d}{c})\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1there are some restrictions on a,b,c,d

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Nice! that wasn't so hard as it appeared to be..

freckles
 one year ago
Best ResponseYou've already chosen the best response.1There are only ways people presented here but I was very much in love with my way http://math.stackexchange.com/questions/1219016/indefiniteintegralwithsinandcos/1219078#1219078

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and no I didn't steal randomgirl 's thoughts :p

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2that is my fav trig identity!

freckles
 one year ago
Best ResponseYou've already chosen the best response.1mine too!! it is super cute.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2wolf's solution isn't bad, it looks pretty long tho
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