A) \[\frac{\sqrt{3}}{2}\]
B) \[\sqrt{3}-1\]
C) \[\frac{1}{2}\]
D) \[\sqrt{2}-1\]
Correct Answer: D
Solution :
Given exp. \[=\cos \theta -\cos 3\theta +\cos \,4\theta \] \[=2\sin 2\theta \sin \theta +\cos 4\theta \] \[[\because \,\theta ={{45}^{o}}]\] \[=2\sin {{90}^{o}}\sin {{45}^{o}}+\cos {{180}^{o}}\] \[=2\times 1\times \frac{1}{\sqrt{2}}-1\] \[=\sqrt{2}-1\]
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