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verify identities solver?

tan2x=(2tanx)/(1-tan^2x)

Use the compound angle formula for the tan function.

I hope you know it, right?

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

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:

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

$\frac{sin(2x)}{cos(2x)}=tan(2x)$

Cos^2x+sin^2x/2sinxcosx

(sin(X))/(tan(X))+(cos(X))/(cot(X))=sin(X)+cos(X)

cos^2x=(1/2)cos2x

Quote:

Originally Posted by mollieblake

cos^2x=(1/2)cos2x

Answered here:
https://www.askmehelpdesk.com/mathem...2x-650298.html

Quote:

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.

cot 2x= cot^2x-1/2cotx

Quote:

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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