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Secant plus tangent of a double angle written as a quotient of sums and differences, then an exact value

Secant plus tangent of a double angle written as a quotient of sums and differences, then an exact value

IB Year 6 | Grade 12
6 marks
  1. Show that \(\sec2x+\tan2x=\frac{\cos x+\sin x}{\cos x-\sin x}\), where \(\cos2x\ne0\).[4]
  2. Deduce the exact value of \(\frac{\cos\frac{\pi}{12}+\sin\frac{\pi}{12}}{\cos\frac{\pi}{12}-\sin\frac{\pi}{12}}\).[2]

Solution:

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Answer:(b) \(\sqrt3\)

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