22) In a triangle \( A B C \) if: \( 3 \sin A=2 \sin B=4 \sin C \), then \( a: b: c= \)

57. Considering the principal values of the inverse trigonometric functions, the sum of all the solutions of the equation is equal to \( \cos ^{-1} x-2 \sin ^{-1} x=\cos ^{-1} 2 x \) \( \begin{array}{ll}\text { (1) } 0 & \text { (2) } 1 \\ \text { (3) } \frac{1}{2} & \text { (4) }-\frac{1}{2}\end{array} \)

\( \tan (x)<\sqrt {3} \)

\( [ \sin - \theta ) + \cos ( 360 - \theta ) ] [ \cos ( 90 - \theta ) + \frac { \sin \theta } { \tan \theta } ] \)

Evaluate \( \frac{\cos 45^{\circ}}{\sec 30^{\circ}+\operatorname{cosec} 30^{\circ}} \)

What is the relationship between the hypotenuse and the adjacent side when defining secant?