Find the principal solutions of the equation $\sin x=\frac{\sqrt{3}}{2}$
Find the principal solutions of the equation $\sin x=\frac{\sqrt{3}}{2}$
We know that, $\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$ and $\sin \frac{2 \pi}{3}=\sin \left(\pi-\frac{\pi}{3}\right)=\sin \frac{\pi}{3}=\frac{\sqrt{3}}{2}$
Therefore, principal solutions are $x=\frac{\pi}{3}$ and $\frac{2 \pi}{3}$.
Similar Questions
In a triangle $P Q R, P$ is the largest angle and $\cos P=\frac{1}{3}$. Further the incircle of the triangle touches the sides $P Q, Q R$ and $R P$ at $N, L$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive even integers. Then possible length$(s)$ of the side$(s)$ of the triangle is (are)
$(A)$ $16$ $(B)$ $18$ $(C)$ $24$ $(D)$ $22$
In a triangle $P Q R, P$ is the largest angle and $\cos P=\frac{1}{3}$. Further the incircle of the triangle touches the sides $P Q, Q R$ and $R P$ at $N, L$ and $M$ respectively, such that the lengths of $P N, Q L$ and $R M$ are consecutive even integers. Then possible length$(s)$ of the side$(s)$ of the triangle is (are)
$(A)$ $16$ $(B)$ $18$ $(C)$ $24$ $(D)$ $22$
- [IIT 2013]
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