problem archive
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Find the value of cos (-1710°). -
Prove that 3\sin\frac{\pi}{6}\sec\frac{\pi}{3}-4\sin\frac{5\pi}{6}\cot\frac{\pi}{4}=1 -
Find the value of \sin 15^\circ. -
Find the value of \tan \frac{13\pi}{12}. -
Prove that \( \frac{\sin(x+y)}{\sin(x-y)} = \frac{\tan x + \tan y}{\tan x - \tan y} \) -
Show that \( \tan 3x \tan 2x \tan x = \tan 3x - \tan 2x - \tan x \) -
Prove that \( \cos \left( \frac{\pi}{4} + x \right) + \cos \left( \frac{\pi}{4} - x \right) = \sqrt{2} \cos x \) -
Prove that \( \frac{\cos 7x + \cos 5x}{\sin 7x - \sin 5x} = \cot x \) -
Prove that \( \frac{\sin 5x - 2\sin 3x + \sin x}{\cos 5x - \cos x} = \tan x \) -
If \sin x = \frac{3}{5}, \cos y = -\frac{12}{13}, where x and y both lie in second quadrant, find the value of \sin (x + y). -
Prove that \cos 2x \cos \frac{x}{2} - \cos 3x \cos \frac{9x}{2} = \sin 5x \sin \frac{5x}{2}. -
Find the value of \( \tan \frac{\pi}{8} \) -
If \( \tan x = \frac{3}{4} \), \( \pi < x < \frac{3\pi}{2} \), find the value of \( \sin \frac{x}{2} \), \( \cos \frac{x}{2} \) and \( \tan \frac{x}{2... -
Prove that \cos^2 x + \cos^2 \left( x + \frac{\pi}{3} \right) + \cos^2 \left( x - \frac{\pi}{3} \right) = \frac{3}{2} -
Find \sin \frac{x}{2}, \cos \frac{x}{2} and \tan \frac{x}{2} in each of the following: -
Solve the equation x^2 + 1 = 0. -
Solve the equation x^2 = -1. -
Solve the equation ax^2 + bx + c = 0, where D = b^2 - 4ac < 0. -
If 4x + i(3x - y) = 3 + i(-6), where x and y are real numbers, then find the values of x and y. -
Express the following in the form of a + bi: (i) (-5i)(1/8)