| If \[\sin 5\theta =\cos 20{}^\circ \,\,(0{}^\circ <\theta <90{}^\circ ),\]then the value of \[\theta \] is [SSG (CGL) Mains 2014] |
A) \[4{}^\circ \]
B) \[22{}^\circ \]
C) \[10{}^\circ \]
D) \[14{}^\circ \]
Correct Answer: D
Solution :
| Given, \[\sin 5\theta =\cos 20{}^\circ \] |
| \[\Rightarrow \]\[\sin 5\theta =\sin \,\,(90{}^\circ -20{}^\circ )\] |
| \[\Rightarrow \] \[5\theta =90{}^\circ -20{}^\circ \] |
| \[\Rightarrow \] \[5\theta =70{}^\circ \] |
| \[\therefore \] \[\theta =14{}^\circ \] |
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