| Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below. |
| Assertion\[\sin \,60{}^\circ =\cos \,30{}^\circ \]. |
| Reason\[\sin \,2\theta =\sin \theta +\sin \theta \], where \[\theta \] is an acute angle. |
A) A is true, R is true; R is a correct explanation for A.
B) A is true, R is true; R is not a correct explanation for A.
C) A is true; R is false.
D) A is false; R is true.
Correct Answer: C
Solution :
| Assertion |
| \[\cos \,30{}^\circ =\frac{\sqrt{3}}{2}\] and \[\sin \,60{}^\circ =\frac{\sqrt{3}}{2}\] |
| Assertion is true |
| Reason \[2\theta =\sin \theta +\sin \theta\] |
| This statement is false for an acute angle. |
| \[\theta =30{}^\circ \Leftrightarrow \sin 2\times 30{}^\circ =\sin 30{}^\circ +\sin 30{}^\circ\] |
| \[\frac{\sqrt{3}}{2}=\frac{1}{2}+\frac{1}{2}\] [False] |
| Assertion is true but Reason is false. |
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