List of top Mathematics Questions on Trigonometric Ratios asked in CBSE CLASS XII

Show that \( f(x) = e^x - e^{-x} + x - \tan^{-1} x \) is strictly increasing in its domain.
If a line makes an angle of \( 30^\circ \) with the positive direction of x-axis, \( 120^\circ \) with the positive direction of y-axis, then the angle which it makes with the positive direction of z-axis is:
(a) Check the differentiability of \( f(x) = | \cos x | \) at \( x = \frac{\pi}{2} \).
The function \( f(x) = x^3 - 3x^2 + 12x - 18 \) is:
If a line makes an angle of \( 30^\circ \) with the positive direction of \( x \)-axis, \( 120^\circ \) with the positive direction of \( y \)-axis, then the angle which it makes with the positive direction of \( z \)-axis is:
If a line makes an angle of \( 30^\circ \) with the positive direction of \( x \)-axis, \( 120^\circ \) with the positive direction of \( y \)-axis, then the angle which it makes with the positive direction of \( z \)-axis is:
The derivative of \( \tan^{-1}(x^2) \) w.r.t. \( x \) is: