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  • Find the value of <img alt="y=\sqrt{3}\ \cos(\frac{\pi}{12})- \sin(\frac{\pi}{12})" src="https://entrancecorner.oncodecogs.com/gif.latex?y%3D%5Csqrt%7B3%7D%5C%20%5Ccos%28%5Cfrac%7B%5Cpi%7D%7B1

Find the value of y=\sqrt{3}\ \cos(\frac{\pi}{12})- \sin(\frac{\pi}{12})

Option: 1

2\sqrt{2}


Option: 2

\sqrt{2}


Option: 3

1/ \sqrt{2}


Option: 4

\frac{1}{2}


Answers (1)

best_answer

\\y = \sqrt{3}\ \cos(\frac{\pi}{12}) - \sin(\frac{\pi}{12})\\ =2[\frac{\sqrt{3}}{2}\ \cos(\frac{\pi}{12}) -\frac{1}{2} \sin(\frac{\pi}{12}) ]\\ =2[\sin(\frac{\pi}{3}) \ \cos(\frac{\pi}{12}) - \cos(\frac{\pi}{3})\sin(\frac{\pi}{12})]\\ =2[\sin(\frac{\pi}{3}-\frac{\pi}{12})]\\ =2[\frac{1}{\sqrt{2}}]\\ =\sqrt{2}

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Anam Khan

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