Trigonometric Functions

Find $\sin \frac{x}{2}$, $\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the following: $\sin x = \frac{1}{4}$, $x$ in quadrant II

Prove that:

$\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$

Prove that: 2sin² π/6 + cosec² 7π/6 cos² π/3 = 3/2

Prove that:

$\cos 6x = 32 \cos^6 x - 48 \cos^4 x + 18 \cos^2 x - 1$

Find the values of other five trigonometric functions: sec x = 13/5, x lies in fourth quadrant.

Find $\sin \frac{x}{2}$, $\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the following: $\tan x = -\frac{4}{3}$, $x$ in quadrant II

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length

Find the values of other five trigonometric functions: sin x = 3/5, x lies in second quadrant.

Find the values of the trigonometric functions: cosec(-1410°)

Prove that:

$\sin(n+1)x \sin(n+2)x + \cos(n+1)x \cos(n+2)x = \cos x$

Prove that:

$\frac{\sin x - \sin y}{\cos x + \cos y} = \tan \frac{x - y}{2}$

Prove that:

$\cos 4x = 1 - 8 \sin^2 x \cos^2 x$

Prove that:

$2 \cos \frac{\pi}{13} \cos \frac{9\pi}{13} + \cos \frac{3\pi}{13} + \cos \frac{5\pi}{13} = 0$

Find $\sin \frac{x}{2}$, $\cos \frac{x}{2}$ and $\tan \frac{x}{2}$ in the following: $\cos x = -\frac{1}{3}$, $x$ in quadrant III.

Prove that:

$(\cos x - \cos y)^2 + (\sin x - \sin y)^2 = 4 \sin^2 \frac{x - y}{2}$

Find the values of the trigonometric functions: tan 19π/3

Find the values of other five trigonometric functions: cot x = 3/4, x lies in third quadrant.

Prove that: 2sin² 3π/4 + 2 cos² π/4 + 2 sec² π/3 = 10

Prove that: sin² π/6 + cos² π/3 - tan² π/4 = -1/2

Prove that:

$\sin 2x + 2 \sin 4x + \sin 6x = 4 \cos^2 x \sin 4x$