# A question on trigonometry!

Find the number of solutions of the equation given below,

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

2 years, 6 months ago

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For real solutions? Answer is 0.

Just apply the Trigonometric R method.

- 2 years, 6 months ago

Thank you very much!

- 2 years, 6 months ago

No, this is the quickest method. $$\quad\quad \quad$$

- 2 years, 6 months 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.

- 2 years, 6 months ago

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

- 2 years, 6 months ago

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

- 2 years, 6 months ago

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

- 2 years, 6 months ago