If \(
\left( x + \frac{1}{x} \right) = 2\sqrt{2}, \quad \text{and } x > 1,
\) what is the value of \( (x^6 - \frac{1}{x^6}) \)
If \(\frac{\sin x - \cos x}{\sin x + \cos x} = \frac{2}{5}\) then , what is the value of \(\frac{1 + \cot^2 x}{1 - \cot^2 x}\)
Study the pie chart and answer the questions
The pie chart displays the % of fruits sold(in kg) by fruit seller in one month
If the total fruits sold by a fruit seller in one month was 50,000 kg, find the approximate difference of the quantity (in kg) of pomegranates and that of berries.
Simplify the given expression
\(\frac{432 \times 432 + 247 \times 247 - 432 \times 247}{432 \times 432 \times 432 + 247 \times 247 \times 247}\)
Simplify the following.
\(\frac{3a + b}{2} - \frac{a - 3b}{3} + 2b\)