Q1.Prove that sec8θ -1 / sec4θ -1 = tan8θ / tan2θ and.........?

Question

Q2.solve the equation tanθ + tan(θ + pi/3) + tan(θ + 2pi/3) = 3

Answer 1

Only one problem per question please.

Prove the identity.
(sec8θ - 1) / (sec4θ - 1) = tan8θ / tan2θ
__________

Left Hand Side = (sec8θ - 1) / (sec4θ - 1)

= [(sec8θ - 1)(cos4θ)] / [(sec4θ - 1)(cos4θ)]

= [(sec8θ - 1)(cos4θ)] / (1 - cos4θ)

= [(sec8θ - 1)(cos4θ)/(sin4θ)] / [(1 - cos4θ)/(sin4θ)]

= [(sec8θ - 1) / tan4θ] / tan2θ

= {[(sec8θ - 1)(cos8θ)] / [(tan4θ)(cos8θ)]} / tan2θ

= {(1 - cos8θ) / [(tan4θ)(cos8θ)]} / tan2θ

= {[(1 - cos8θ)/(sin8θ)] / [(tan4θ)(cos8θ)/(sin8θ)]} / tan2θ

= {(tan4θ) / [tan4θ / tan8θ]} / tan2θ

= tan8θ / tan2θ = Right Hand Side

Answer 2

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