: Prove that: (sec8theta-1)/(sec8theta+1)=tan8theta/tan2thetapdegk,oegjmirjnhrfyfgrrrrrtggbfrrhbhrfdtdjutyjffhdzsarfyrehyefearryhrtjghfxndgaweftdhgr

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LHS=(sec 8θ -1 )/ (sec4θ -1)

=(1/(cos8θ) -1 )/ (1/(cos4θ) -1)

=((1-cos8θ)cos4θ )/ ((1-cos4θ) cos8θ)

=(2sin24θcos4θ )/ ((2sin22θ) cos8θ)

=(2sin4θcos4θsin4θ )/ ((2sin22θ) cos8θ)

=(sin8θ * 2sin2θcos2θ )/ ((2sin22θ) cos8θ)

=(tan8θ * cos2θ )/ (sin2θ)

= (tan8θ) /(tan 2θ)

= RHS

Hence proved.

Thanks