How do you verify the identity #sec^4theta-tan^4theta=1+2tan^2theta#?

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Answer 1 · 2017-02-08T15:51:41

see below

Left Hand Side:

Use the identity:
#1+tan^2 theta=sec^2 theta#

#sec^4 theta - tan^4 theta=(sec^2theta-tan^2theta)(sec^2theta+tan^2theta)#

#=1(sec^2theta+tan^2theta)#

#=sec^2theta+tan^2theta#

#=1+tan^2 theta + tan^2 theta#

#=1+2tan^2 theta#

#:.=# Right Hand Side