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

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Answer 1 · 2016-09-07T14:38:40

See the Explanation.

We will use the Identity # : sec^2x=1+tan^2x#.

#"The R.H.S."=2sec^2theta-sec^4theta#

#=sec^2theta(2-sec^2theta)#

#=(1+tan^2theta){1+(1-sec^2theta)}#

#=(1+tan^2theta){1-(sec^2theta-1)}#

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

#=1^2-(tan^2theta)^2#

#=1-tan^4theta#

#"=The L.H.S."#