Prove that : sec 8 theta-1/sec 4 theta-1 = tan 8 theta/tan 2 theta

1.	Prove that : sec 8 theta-1/sec 4 theta-1 = tan 8 theta/tan 2 theta
Answer» sec8θ−1/sec4θ−1\xa0=tan8θ/tan2θOr\xa0sec8θ−1/tan8θ=sec4θ−1/tan2θLHS\xa0=1/cos8θ−1/sin8θ/cos8θ=1−cos8θ/sin8θ =2sin2(4θ)/2sin4θcos4θ\xa0=tan4θRHS=sec4θ−1/tan2θ\xa0=1/cos4θ−1/tan2θ=1−cos4θ/cos4θ(tan2θ)=2sin2(2θ)cos4θ×sin2θcos2θ=2sin2θcos2θcos4θ=sin4θ/cos4θ=\xa0tan4θ\xa0=\xa0LHS

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