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A question on trigonometry!

Find the number of solutions of the equation given below,

\(\sqrt{3}\sin \theta+ \cos \theta = 4\)

Note by Akshay Yadav
9 months ago

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For real solutions? Answer is 0.

Just apply the Trigonometric R method. Pi Han Goh · 9 months ago

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@Pi Han Goh Thank you very much! Akshay Yadav · 9 months ago

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@Akshay Yadav No, this is the quickest method. \(\quad\quad \quad\) Pi Han Goh · 9 months ago

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Since the maximum real value for \(\sin \theta\) and \(\cos \theta\) is \(1\), LHS cannot be larger than \(\sqrt{3}+1 < 4\), therefore, there is no real root. Chew-Seong Cheong · 9 months ago

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@Chew-Seong Cheong Your method is right, but the maximum value of LHS is not \(\sqrt3+1\). Aditya Agarwal · 8 months, 3 weeks ago

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@Aditya Agarwal I did not say that the maximum value is \(\sqrt{3}+1\). What I meant was LHS \(\ne\) RHS. Chew-Seong Cheong · 8 months, 3 weeks ago

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@Chew-Seong Cheong Thanks! I also used the same method to solve the question in exam and wondering if it was correct or not. Akshay Yadav · 9 months ago

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