3.7: Cosec–sec–tan simplifies to sine

0606/22/F/M/23 — Question 4 · 4 marks

y=cosec 5x−sec 5x tan 5xy = \mathrm{cosec}\,5x - \mathrm{sec}\,5x\,\mathrm{tan}\,5x
Show that y=a sin bxy = a\,\mathrm{sin}\,bx, where aa and bb are integers, and hence find the value of ∫0π/5y dx\displaystyle\int_{0}^{\pi/5} y\,\mathrm{d}x.
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