| If \[\sin 5\theta =\cos 30{}^\circ \,\,(0{}^\circ <\theta <90{}^\circ ),\]then the value of \[\theta \] is |
A) \[12{}^\circ \]
B) \[13{}^\circ \]
C) \[14{}^\circ \]
D) \[15{}^\circ \]
Correct Answer: A
Solution :
| \[\sin 5\theta =\cos 30{}^\circ \] |
| \[\Rightarrow \]\[\sin 5\theta =\sin \,(90{}^\circ -30{}^\circ )\] |
| \[\Rightarrow \]\[\sin 5\theta =\sin 60{}^\circ \] |
| \[\Rightarrow \]\[5\theta =60{}^\circ \]\[\Rightarrow \]\[\theta =12{}^\circ \] |
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