In a circular of diameter 40 cm, a chord is of length 20 cm. FInd the length of the minor arc of the chord?

A train is moving on a circular track of 1500 m radius at the rate of 66 Km/hr. What angle will it turn in 20 seconds?

Prove that cos (A + B) cos C - cos (B + c) cos A = sin B sin (C - A)

Find the degree measure of the angle subtended at the center of circle of radius 100 cm by an arc of length 22 cm.

Prove that sin² (A + B) - sin² (A - B) = sin 2A sin 2B

The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degree, minites and seconds,

If tan x = \(\frac{n}{n+1}\) and tan y = \(\frac{1}{2n+1}\), find tan (x + y).

If \(\theta +\phi =\alpha\)  and \(tan​​\theta=k\ \tan\ \phi \) then prove that \(\sin { \left( \theta -\phi \right) } =\frac { k-1 }{ k+1 } \sin { \alpha } \).

\(\left( \frac { 5 }{ 7 } ,\frac { 2\sqrt { 6 } }{ 7 } \right) \) is a point on the terminal side of an angle \(\theta\) in standard position. Determine the six trigonometric function values of angle \(\theta\)

If \(\theta\) is an acute angle, then find \(\sin { \left( \frac { \pi }{ 4 } -\frac { \theta }{ 2 } \right) } \), when \(\sin { \theta } =\frac { 1 }{ 25 } \)