A binary operation * is defined on the set of real numbers R, by a* b = -1. Find the identity element under the operation *.
Express 75° in radians, leaving your answer in terms of \(\pi\).
If \(\log_{9} 3 + 2x = 1\), find x.
Evaluate \(\cos (\frac{\pi}{2} + \frac{\pi}{3})\)
Find the remainder when \(5x^{3} + 2x^{2} - 7x - 5\) is divided by (x - 2).
