jasonbr Posts: 1, Reputation: 1 New Member #1 Jan 28, 2011, 07:07 AM
verify identities solver?
tan2x=(2tanx)/(1-tan^2x)
 Unknown008 Posts: 8,076, Reputation: 723 Uber Member #2 Jan 28, 2011, 07:28 AM

Use the compound angle formula for the tan function.

I hope you know it, right?
 galactus Posts: 2,271, Reputation: 282 Ultra Member #3 Jan 28, 2011, 07:32 AM

$tan(2x)=\frac{2tan(x)}{1-tan^{2}(x)}$

When proving trig identities, try getting into the habit of converting everything to sin and cos.

$\frac{sin(2x)}{cos(2x)}=\frac{\frac{2sin(x)}{cos(x )}}{1-\frac{sin^{2}(x)}{cos^{2}(x)}}$

The right side becomes:

$\frac{\frac{2sin(x)}{cos(x)}}{\frac{cos^{2}(x)-sin^{2}(x)}{cos^{2}(x)}}$

$\frac{2sin(x)}{\not{c}\not{o}\not{s} \not{x}} \cdot \frac{cos^{\not{2}^{1}}(x)}{cos^{2}(x)-sin^{2}(x)}$

Now, knowing that $cos^{2}(x)-sin^{2}(x)=cos(2x)$

and $sin(2x)=2sin(x)cos(x)$

we get:

$2sin(x)\cdot\frac{cos(x)}{cos(2x)}$

$\frac{sin(2x)}{cos(2x)}=tan(2x)$
 chylathomas Posts: 1, Reputation: 1 New Member #4 Dec 2, 2011, 08:02 AM
Cos^2x+sin^2x/2sinxcosx
 ampomaah Posts: 1, Reputation: 1 New Member #5 Feb 28, 2012, 10:57 PM
(sin(X))/(tan(X))+(cos(X))/(cot(X))=sin(X)+cos(X)
 mollieblake Posts: 2, Reputation: 1 New Member #6 Apr 11, 2012, 09:00 PM
cos^2x=(1/2)cos2x
 ebaines Posts: 12,132, Reputation: 1307 Expert #7 Apr 12, 2012, 10:47 AM
Originally Posted by mollieblake
cos^2x=(1/2)cos2x
 ebaines Posts: 12,132, Reputation: 1307 Expert #8 Apr 12, 2012, 10:49 AM
Originally Posted by ampomaah
(sin(X))/(tan(X))+(cos(X))/(cot(X))=sin(X)+cos(X)
Simply convert the tan(x) and cot(x) functions to their sine and cosine equivalents, and it comes right out.
 mackenzielech Posts: 1, Reputation: 1 New Member #9 Feb 20, 2013, 07:03 PM
cot 2x= cot^2x-1/2cotx
 ebaines Posts: 12,132, Reputation: 1307 Expert #10 Feb 21, 2013, 05:51 AM
Originally Posted by mackenzielech
cot 2x= cot^2x-1/2cotx
No, the identity is incorrect: $cot(2x) \ \ne \ cot^2(x) - \frac 12 cot(x)$

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