How do you prove #csc^4[theta]-cot^4[theta]=2csc^2-1#?

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Answer 1 · 2016-05-02T21:05:40

See Below

Left Side: #=csc^4 theta - cot^4 theta#

#=1/sin^4 theta - cos^4 theta /sin^4 theta#

#=(1-cos^4 theta)/sin^4 theta#

#=((1+cos^2 theta)(1-cos^2 theta))/sin^4 theta#

#=((1+cos^2 theta)sin^2 theta)/sin^4 theta#

#=(1+cos^2 theta)/sin^2 theta#

#=1/sin^2 theta + cos^2 theta/sin^2 theta#

#=csc^2 theta +cot^2 theta#---> #cot^2 theta = csc^2 theta -1#

#=csc^2 theta+csc^2 theta -1#

#=2csc^2 theta -1#

#=#Right Side