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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
1 year, 11 months ago

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For real solutions? Answer is 0.

Just apply the Trigonometric R method.

Pi Han Goh - 1 year, 11 months ago

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Thank you very much!

Akshay Yadav - 1 year, 11 months ago

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No, this is the quickest method. \(\quad\quad \quad\)

Pi Han Goh - 1 year, 11 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 - 1 year, 11 months ago

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Your method is right, but the maximum value of LHS is not \(\sqrt3+1\).

Aditya Agarwal - 1 year, 10 months ago

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I did not say that the maximum value is \(\sqrt{3}+1\). What I meant was LHS \(\ne\) RHS.

Chew-Seong Cheong - 1 year, 10 months ago

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Thanks! I also used the same method to solve the question in exam and wondering if it was correct or not.

Akshay Yadav - 1 year, 11 months ago

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