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

Question

16388 views around the world

You can reuse this answer
Creative Commons License

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)#