exam Maths Puzzle Numerical Ability

Prove the following identity:

sin(2t) = 2 * ((cot(t))/(1 +cot^2(t)))

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exam Other Question

Can you please help me solve: In a golden rectangle the ratio of the length to the width equals the ratio of the length plus width to the length. Find the value of this golden ratio. (do not approximate the answer) can you help me?