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We have 2tan(th) / (1 + tan^2(th)) = sin(2th)

We know that tan(A) = sin(A) / cos(A), and 1 + tan^2(A) = sec^2(A)

Therefore => (2sin(th) / cos(th)) / sec^2(th)

=> 2sin(th)*cos^2(...

Oxbridge medical questions look for 'how you think' rather than knowledge above A-level standard. For a particular topic, they may start on A-level material to warm you up, and then ask follow-up question...

We have 3^(2x+1) = 4^100

=> log(3^(2x+1)) = log(4^100)

=> (2x+1)log(3) = 100log(4)

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Transverse wave - electromagnetic wave, waves on a string Longitudinal wave - sound wave, seismic P-waves