1. trigonometry Prove indentity

[IMG]file:///C:/DOCUME%7E1/Asus/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG]Cotx - tanx = 2cot2x

2. Originally Posted by manutd4life
[IMG]file:///C:/DOCUME%7E1/Asus/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG]Cotx - tanx = 2cot2x

You need to know that

$\cos^2{x} - \sin^2{x} = \cos{2x}$

and

$2\sin{x}\cos{x} = \sin{2x} \implies \sin{x}\cos{x} = \frac{1}{2}\sin{2x}$.

These are proved using the sum formulas (which are proven here)

Proof of the sum and difference formulas.

Trigonometric identities

$\cot{x} - \tan{x} = \frac{\cos{x}}{\sin{x}} - \frac{\sin{x}}{\cos{x}}$

$= \frac{\cos{x}}{\sin{x}}\times\frac{\cos{x}}{\cos{x }} - \frac{\sin{x}}{\cos{x}}\times\frac{\sin{x}}{\sin{x }}$

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

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

$= \frac{2\cos{2x}}{\sin{2x}}$

$= 2\cot{2x}$.

3. i have not understand this part clearly
Originally Posted by Prove It

$= \frac{\cos{x}}{\sin{x}}\times\frac{\cos{x}}{\cos{x }} - \frac{\sin{x}}{\cos{x}}\times\frac{\sin{x}}{\sin{x }}$

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

$= \frac{\cos^2{x} - \sin^2{x}}{\frac{1}{2}\sin{2x}}$
please help how u got this ${\frac{1}{2}\sin{2x}}$

4. Originally Posted by manutd4life
i have not understand this part clearly

please help how u got this ${\frac{1}{2}\sin{2x}}$
$\frac{\cos^2{x}}{\sin{x}\cos{x}} - \frac{\sin^2{x}}{\sin{x}\cos{x}} = \frac{\cos^2{x}-\sin^2{x}}{\sin{x}\cos{x}} = \frac{\cos{2x}}{\frac{1}{2}\sin{2x}}$

5. Thank you very much

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