Find the number of solutions of the equation given below,

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

Find the number of solutions of the equation given below,

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

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TopNewestFor real solutions? Answer is 0.

Just apply the Trigonometric R method. – Pi Han Goh · 1 year, 3 months ago

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– Akshay Yadav · 1 year, 3 months ago

Thank you very much!Log in to reply

– Pi Han Goh · 1 year, 3 months ago

No, this is the quickest method. \(\quad\quad \quad\)Log in to reply

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, 3 months ago

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– Aditya Agarwal · 1 year, 3 months ago

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

– Chew-Seong Cheong · 1 year, 3 months ago

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

– Akshay Yadav · 1 year, 3 months ago

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