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# A question on trigonometry!

Find the number of solutions of the equation given below,

$$\sqrt{3}\sin \theta+ \cos \theta = 4$$

1 year ago

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For real solutions? Answer is 0.

Just apply the Trigonometric R method. · 1 year ago

Thank you very much! · 1 year ago

No, this is the quickest method. $$\quad\quad \quad$$ · 1 year ago

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. · 1 year ago

Your method is right, but the maximum value of LHS is not $$\sqrt3+1$$. · 1 year ago

I did not say that the maximum value is $$\sqrt{3}+1$$. What I meant was LHS $$\ne$$ RHS. · 1 year ago