How do I prove this identity? 2-tanx/2cscx-secx=Sinx

1 Answer
May 12, 2018

See below

Explanation:

Using identities:
#tanx=sinx/cosx#
#secx=1/cosx#
#cscx=1/sinx#

Start:

#( 2-tanx)/(2cscx-secx)=Sinx#

#( (2cosx)/cosx-sinx/cosx)/(2/sinx-1/cosx)=Sinx#

#( (2cosx)/cosx-sinx/cosx)/((2cosx)/(sinxcosx)-sinx/(sinxcosx))=Sinx#

#( (2cosx-sinx)/cosx)/((2cosx-sinx)/(sinxcosx))=Sinx#

#cancel(2cosx-sinx)/cancelcosx*(sinxcancelcosx)/cancel(2cosx-sinx)=Sinx#

#sinx=sinx#