10th Class Mathematics Introduction to Trigonometry Question Bank MCQs - Introduction to Trigonometry

If \[\sqrt{2}\,\sin (60{}^\circ -\alpha )=1,\]then \[\alpha \] is: (CBSE 2011)

A) \[45{}^\circ \]

B) \[15{}^\circ \]

C) \[60{}^\circ \]

D) \[30{}^\circ \]

Correct Answer: B

Solution :

[b] \[\sqrt{2}\,\,\sin \,(60{}^\circ -\alpha )=1\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\sin (60{}^\circ -\alpha )=\frac{1}{\sqrt{2}}=\sin 45{}^\circ \]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,60{}^\circ -\alpha =45{}^\circ \,\,\,\,\,\Rightarrow \,\,\,\,\alpha =15{}^\circ \]