What is #cottheta-csctheta-costheta# in terms of #sintheta#?

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Answer 1 · 2015-12-09T01:05:13

#(costheta-costhetasintheta-1)/sintheta, theta!=0^@, 180^@, 360^@#

Recall:
#1. cotx=1/tanx# or #cosx/sinx#
#2. cscx=1/sinx#

Substitute your reciprocal and quotient identities into the equation:

#cottheta-csctheta-costheta#

#=costheta/sintheta-1/sintheta-costheta#

#=(costheta-1-costheta(sintheta))/sintheta#

#=(costheta-1-costhetasintheta)/sintheta#

#=(costheta-costhetasintheta-1)/sintheta, theta!=0^@, 180^@, 360^@#