| The value of \[(\cos 0{}^\circ +\sin 45{}^\circ +\sin 30{}^\circ )\]\[(sin90{}^\circ -cos45{}^\circ +\cos 60{}^\circ )\]is |
A) \[\frac{3}{2}\]
B) \[\frac{7}{4}\]
C) \[\frac{5}{4}\]
D) \[\frac{3}{4}\]
Correct Answer: B
Solution :
| \[(\cos 0{}^\circ -\sin 45{}^\circ +\sin 30{}^\circ )\] |
| \[(\sin 90{}^\circ -\cos 45{}^\circ +\cos 60{}^\circ )\] |
| \[=\left( 1+\frac{1}{\sqrt{2}}+\frac{1}{2} \right)\left( 1-\frac{1}{\sqrt{2}}+\frac{1}{2} \right)\] |
| \[=\left( \frac{3}{2}+\frac{1}{\sqrt{2}} \right)\left( \frac{3}{2}-\frac{1}{\sqrt{2}} \right)\] |
| \[={{\left( \frac{3}{2} \right)}^{2}}-{{\left( \frac{1}{\sqrt{2}} \right)}^{2}}=\frac{9}{4}-\frac{1}{2}=\frac{9-2}{4}=\frac{7}{4}\] |
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