Question : If $\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}=c$, then the value of $\mathrm{c}$ is:
Option 1: 1
Option 2: 4
Option 3: 3
Option 4: 2
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Correct Answer: 1
Solution : Given: $\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}=c$ Squaring both sides, we get ⇒ $\left (\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}\right ) ^2=c^2$ ⇒ $1+\frac{\sqrt{3}}{2}+1-\frac{\sqrt{3}}{2}-2\times\sqrt{1-\frac{3}{4}}=c^2$ ⇒ $2-2\times\sqrt{\frac{1}{4}}=c^2$ ⇒ $2-2\times\frac{1}{2}=c^2$ ⇒ $2-1=c^2$ ⇒ $c=1$ Hence, the correct answer is 1.
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Question : If $\mathrm{p}=\frac{\sqrt{2}+1}{\sqrt{2}-1}$ and $\mathrm{q}=\frac{\sqrt{2}-1}{\sqrt{2}+1}$ then, find the value of $\frac{\mathrm{p}^2}{\mathrm{q}}+\frac{\mathrm{q}^2}{\mathrm{p}}$.
Question : If $c+ \frac{1}{c} =\sqrt{3}$, then the value of $c^{3}+ \frac{1}{c^{3}}$ is equal to:
Question : If $\sec ^2 \mathrm{~A}+\tan ^2 \mathrm{~A}=3$, then what is the value of $\cot \mathrm{A}$?
Question : If $\frac{\sqrt{26-7 \sqrt{3}}}{\sqrt{14+5 \sqrt{3}}}=\frac{b+a \sqrt{3}}{11}, b>0$, then what is the value of $\sqrt{(\mathrm{b}-\mathrm{a})}$?
Question : If $\mathrm{p}=7+4 \sqrt{3}$, then what is the value of $\frac{\mathrm{p}^6+\mathrm{p}^4+\mathrm{p}^2+1}{\mathrm{p}^3}$?
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