How do you express #f(theta)=sin^2(theta)+3cot^2(theta)-3csc^2theta# in terms of non-exponential trigonometric functions?

1 Answer
P dilip_k
Feb 19, 2016

see below

Explanation:

#f(theta)=# #3sin^2theta+3cot^2theta-3csc^2theta#
=#3sin^2theta+3cot^2theta-3csc^2theta#
=#3sin^2theta+3(csc^2theta-1)-3csc^2theta#
=#3sin^2theta+cancel(3csc^2theta)-cancel3csc^2theta-3#
=#3sin^2theta-3#
=-3 #(1-sin^2theta)#
=#-3cos^2theta#

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