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O-Level Trigonometric functions, identities and equations: worked solution
3 marks. Full working, one step per line.
Question
Show, without the use of a calculator, that tan 285° = (√3 + 1)/(1 − √3).
Worked answer
285° = 360° - 75°, so tan 285° = tan(-75°) = -tan 75°. tan 75° = tan(45° + 30°) = (tan45° + tan30°)/(1 - tan45°·tan30°) = (1 + 1/√3)/(1 - 1/√3) = (√3 + 1)/(√3 - 1). Therefore tan 285° = -(√3 + 1)/(√3 - 1) = (√3 + 1)/(1 - √3).
Practise this topic
This question is part of O-Level Trigonometric functions, identities and equations, in O-Level Additional Maths (A-Maths).
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