Without using a calculator, and showing all your working, find the exact value of \(\sin\dfrac\pi4\cos\dfrac{5\pi}{12}+\cos\dfrac\pi4\sin\dfrac{5\pi}{12}\).[2]
Given that \(\tan\theta=k\) and that \(\theta\) is acute, express in terms of \(k\)
\(\sec\theta\),[2]
\(\sin2\theta\).[2]
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Answer:(a) \(\dfrac{\sqrt3}2\). (b)(i) \(\sqrt{1+k^2}\), (ii) \(\dfrac{2k}{1+k^2}\).