How do you simplify $tan x / (1-cos^2 x)$ ?

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Answer 1 · 2016-08-23T15:46:39

$tanx/(1-cos^2x)=1/(sinxcosx)==secxcscx=2csc2x$ .

$tanx/(1-cos^2x)=tanx/sin^2x=(sinx/cosx)/sin^2x=sinx/cosx*1/sin^2x$

$=1/(sinxcosx), or, =secxcscx$

Since,

$sin2x=2sinxcosx, "the above can further be expressed as" 2/(2sinxcosx)=2csc2x$ .

Enjoy Maths.!

Answer 2 · 2016-08-23T15:54:03

$1/(sinxcosx)$

$tanx=sinx/cosx$

The one identity that you need to remember is
$sin^2x+cos^2x=1$

all the others can be deduced from this

So $1-cos^2x=sin^2x$

Therefore the original expression can be written as

$sinx/(cosxsin^2x)$

Cancelling gives
$1/(sinxcosx)$

How do you simplify tan x / (1-cos^2 x)tan x / (1-cos^2 x)?