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

If \[\sin x+\cos y=1,\]\[x=30{}^\circ \]and y is an acute angle then the value of y is:

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

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

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

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

Correct Answer: D

Solution :

[d] Given \[\sin x+\cos y=1\]

Put \[x=30{}^\circ \]

\[\sin 30{}^\circ +\cos y=1\,\,\Rightarrow \,\,\cos y=1-\frac{1}{2}\,\,(\sin 30{}^\circ =1/2)\]

\[\Rightarrow \,\,\,\,\cos y=\frac{1}{2}\,\,\,\,\,\,\,\Rightarrow \,\,\,\,\,\,y=60{}^\circ \,\,\,\,\,(\cos 60{}^\circ \,\,=1/2)\]