How do you verify the identity #csc^4theta-cot^4theta=2csc^2theta-1#?

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Answer 1 · 2017-04-19T06:34:06

see below

Use the Pythagorean Identity
#color(red)(cot^2 theta+1=csc^2 theta#

#color(red)(cot^2 theta=csc^2 theta-1#--->isolate #cot^2 theta#

#color(red)(1=csc^2 theta-cot^2 theta#---> isolate 1

Left Hand Side:

#color(red)(csc^4 theta-cot^4 theta=color(blue)((csc^2 theta+cot^2 theta)(csc^2 theta-cot^2 theta)#

#color(blue)(=(csc^2 theta+cot^2 theta)*1#

#color(blue)(=csc^2 theta+cot^2 theta#

#color(blue)(=csc^2 theta+csc^2 theta-1#

#color(blue)(=2csc^2 theta-1#

#color(blue)(=#Right Hand Side