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Question:
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Consider the following statements:
1. If $3 \theta$ is an acute angle such that $\sin 3 \theta=\cos 2 \theta$, then
the mesurement of $\theta$ in radian equals to $\frac{\pi}{10}$.
2 One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle. Which of the above statements is/are correct?
Options:
1. If $3 \theta$ is an acute angle such that $\sin 3 \theta=\cos 2 \theta$, then
the mesurement of $\theta$ in radian equals to $\frac{\pi}{10}$.
2 One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to the diameter of that circle. Which of the above statements is/are correct?
Solution:
2939 Upvotes
Verified Answer
The correct answer is:
1 only
Statement: 1 $\sin 3 \theta=\cos 2 \theta$
$\sin 3 \theta=\sin \left(\frac{\pi}{2}-2 \theta\right)$
$3 \theta=\frac{\pi}{2}-2 \theta$
$5 \theta=\frac{\pi}{2} \Rightarrow \theta=\frac{\pi}{10}$
Statement : 2 One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to radius of that circle. Hence, statement 1 is correct.
$\sin 3 \theta=\sin \left(\frac{\pi}{2}-2 \theta\right)$
$3 \theta=\frac{\pi}{2}-2 \theta$
$5 \theta=\frac{\pi}{2} \Rightarrow \theta=\frac{\pi}{10}$
Statement : 2 One radian is the angle subtended at the centre of a circle by an arc of the same circle whose length is equal to radius of that circle. Hence, statement 1 is correct.
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