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from chapter trigonometry class 11
prove that LHS=RHS
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LHS:
(sec8θ-1)/(sec4θ-1)
=(1/cos8θ-1)/(1/cos4θ-1)
=[(1-cos8θ)/cos8θ]/[(1-cos4θ)/cos4θ]
=(2sin²4θ/cos8θ)/(2sin²2θ/cos4θ) [∵, 1-cos2θ=2sin²θ]
=2(2sin2θcos2θ)²/cos8θ×cos4θ/2sin²2θ
=4cos²2θcos4θ/cos8θ
RHS:
tan8θ/tan2θ
=(sin8θ/cos8θ)/(sin2θ/cos2θ)
=2sin4θcos4θ/cos8θ×cos2θ/sin2θ
=2.2sin2θcos2θcos4θ/cos8θ×cos2θ/sin2θ
=4cos²2θcos4θ/cos8θ
∴ LHS=RHS
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