Prove that sec(2theta)=sec^2(theta) divided by (2-sec^2(theta))?

Question

Prove #sec2theta=sec^2theta/(2-sec^2theta)#

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Answer 1 · 2018-02-12T01:04:27

#LHS=sec2theta#

#=1/(cos2theta)#

#=1/(2cos^2theta-1)#

#=(1/cos^2theta)/((2cos^2theta)/cos^2theta-1/cos^2theta)#

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

Note

#cos2theta=cos(theta+theta) #

#=costheta costheta-sinthetasintheta#
#=cos^2theta -sin^2theta#

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

#=2 cos^2theta-1#