×

# A question on trigonometry!

Find the number of solutions of the equation given below,

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

11 months, 2 weeks ago

Sort by:

For real solutions? Answer is 0.

Just apply the Trigonometric R method. · 11 months, 2 weeks ago

Thank you very much! · 11 months, 2 weeks ago

No, this is the quickest method. $$\quad\quad \quad$$ · 11 months, 2 weeks 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. · 11 months, 2 weeks ago

Your method is right, but the maximum value of LHS is not $$\sqrt3+1$$. · 11 months, 1 week ago

I did not say that the maximum value is $$\sqrt{3}+1$$. What I meant was LHS $$\ne$$ RHS. · 11 months, 1 week ago