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

2 Answers
Aug 23, 2016

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

Explanation:

#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.!

Aug 23, 2016

#1/(sinxcosx)#

Explanation:

#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)#