Here is a tricky A-level maths question in which you are asked to prove that
tan 50 = tan 40 +2tan 10
Try it first and can you comment on the difficulty. Thanks.
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Thank you for posting this problem. It looks difficult at first, but once you've realized that 40 and 50 are complementary angles, it becomes very easy to prove. My proof of the more general case: alpha+beta = 90, tan(alpha) = tan(beta)+2tan(alpha-beta), is three lines. Just use tan(beta) = cot(alpha), the formula for tan(alpha-beta) and tan(alpha)cot(alpha)=1.<br /> It is a good problem for practising properties of complementary angles. My A-level students will be glad I've found something challenging.
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