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Differentiation of Inverse Trigonometric Functions

Solve the fol...

Question

Solve the following:
${⎛ ⎝ \sqrt{{(\sqrt{5} - \frac{5}{2})}^{2}} - \sqrt[3]{{(\frac{3}{2} - \sqrt{5})}^{3}} ⎞ ⎠}^{1 / 2} - \sqrt{2} sin \frac{7 π}{4}$

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Solution

$((\sqrt{5} - \frac{5}{2})^{2 \times \frac{1}{2}}$ - $(\frac{3}{2} - \sqrt{5})^{3 \times \frac{1}{3}})^{\frac{1}{2}}$ - $\sqrt{2} s i n (2 π - \frac{π}{4})$
$(\sqrt{5} - \frac{5}{2} - \frac{3}{2} + \sqrt{5})^{\frac{1}{2}} - \sqrt{2} \times - \sqrt{2}$
$(2 \sqrt{5} - 4)^{\frac{1}{2}} + 2$

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Q. Solve the following:

{⎛ ⎝ \sqrt{{(\sqrt{2} - \frac{3}{2})}^{2}} - \sqrt[3]{(1 - \sqrt{2})^{3}} ⎞ ⎠}^{2} + 2^{- \frac{3}{2}} cos \frac{3 π}{4}

Q. Observe the following pattern

(1 \times 2) + (2 \times 3) = \frac{2 \times 3 \times 4}{3}

(1 \times 2) + (2 \times 3) + (3 \times 4) = \frac{3 \times 4 \times 5}{3}

(1 \times 2) + (2 \times 3) + (3 \times 4) + (4 \times 5) = \frac{4 \times 5 \times 6}{3}

and find the value of
(1 × 2) + (2 × 3) + (3 × 4) + (4 × 5) + (5 × 6)

2 \frac{2}{5} + 1 \frac{2}{3} - \frac{2}{6}

Q. Solve the following equations:

5 \sqrt{\frac{3}{x}} + 7 + \sqrt{\frac{x}{3}} = 22 \frac{2}{3}

Q. Solve the following equation:

\frac{4}{\sqrt[3]{x} + 2} + \frac{\sqrt[3]{x} + 3}{5} = 2

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