Question : If $\mathrm{A}=22.5^{\circ}$, what is the value of $(10 \sqrt{2} \sin 2\mathrm{A}-7 \sqrt{2} \cos 2\mathrm{A}+9 \tan 2\mathrm{A})$?
Option 1: 12
Option 2: 15
Option 3: 10
Option 4: 6
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Correct Answer: 12
Solution :
Given: $\mathrm{A}=22.5^{\circ}$
We have to find the value of $(10 \sqrt{2} \sin 2 \mathrm{~A}-7 \sqrt{2} \cos 2 \mathrm{~A}+9 \tan 2 \mathrm{~A})$
= $(10 \sqrt{2} \sin 2 \mathrm{(22.5^{\circ})}-7 \sqrt{2} \cos 2 \mathrm{(22.5^{\circ})}+9 \tan 2 \mathrm{(22.5^{\circ})})$
= $(10 \sqrt{2} \sin \mathrm{45^{\circ}}-7 \sqrt{2} \cos \mathrm{45^{\circ}}+9 \tan \mathrm{45^{\circ}})$
= $(10 \sqrt{2}\times{\frac{1}{\sqrt{2}}}-7 \sqrt{2}\times{\frac{1}{\sqrt{2}}} +9 )$
= (10 – 7 + 9)
= 12
Hence, the correct answer is 12.
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