Proving identity #1

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April 9th 2009, 02:12 PM
skeske1234

Proving identity #1

cotx+tanx=2csc2x

LS:

cotx+tanx
=cosx/sinx+sinx/cosx
=1/cosxsinx

RS:

2csc2x
=2(1/sin)2x

What should I do now?
April 9th 2009, 02:27 PM
masters

Quote:

Originally Posted by skeske1234

$\cot x+\tan x=2\csc 2x$

LS:

$\cot x+\tan x=$

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

${\color{red}\frac{1}{\sin x \cos x}=}$

RS:

Try this instead: Recall that $\sin 2x = 2 \sin x \cos x$

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

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

${\color{red}=\frac{1}{\sin x \cos x}}$

..
April 9th 2009, 02:33 PM
skeeter

Quote:

Originally Posted by skeske1234

cotx+tanx=2csc2x

LS:

cotx+tanx
=cosx/sinx+sinx/cosx
=1/cosxsinx ... multiply numerator and denominator by 2

RS:

2csc2x
=2(1/sin)2x ... 2/[sin(2x)]

What should I do now?

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