Question #d92c6

1 Answer
ErmWhat
Sep 22, 2017

Proving the identity will not fit in the answer, so look below.

Explanation:

So, we are trying to prove this: #tanx-cscxsecx(1-2cos^2x)=cotx#
Using this proof: #sin^2 x + cos^2x=1#...
#tanx-cscxsecx(sin^2x+cos^2x-2cos^2x)=cotx#
#tanx-cscxsecx(sin^2x-cos^2x)=cotx#

Using these proofs: #tanx = sinx/cosx#, #cscx=1/sinx# and #secx=1/cosx#.
#sinx/cosx-1/(sinxcosx)(sin^2x-cos^2x)=cotx#
#sinx/cosx-(sin^2x-cos^2x)/(sinxcosx)=cotx#

Make both denominators the same on the left side only... (we leave the right side alone for proofs).
#(sin^2x-(sin^2x-cos^2x))/(sinxcosx)=cotx#
#(sin^2x-sin^2x+cos^2x)/(sinxcosx)=cotx#
#(cos^2x)/(sinxcosx)=cotx#
#(cosx)/(sinx)=cotx#

Use this proof: #cosx/sinx = cotx#
#cotx=cotx#

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