Establish the identity sin 7x sin 3xcos 7x cos 3x tan 5x

Establish the identity sin 7x + sin 3x/cos 7x + cos 3x = tan (5x). Which of the following statements establishes the identity? sin 7x + sin 3x/cos 7x + cos 3x = 2 sin 7x - 3x/2 cos 7x + 3x/2/2 cos 7x - 3x/2 cos 7x + 3x/2 = sin 7x + 3x/2 7x + 3x/cos 2 = tan(5x) B. sin 7x + sin 3x/cos 7x + cos 3x = 2 sin 7x + 3x/2 cos 7x - 3/2/2 cos 7x + 3x/2 cos 7x - 3x/2 = sin 7x + 3x/2/7x + 3x/cos 2 = tan(5x) C. sin 7x + sin 3x/cos 7x + cos 3x = 2 sin 7x - 3x/2 cos 7x + 3x/2 sin 7x + 3x/2/2 cos 7x + 3x/2 cos 7x - 3x/2 cos 7x + 3x/2

Solution

given

sin(7x) + sin(3x) 2 sin (7x + 3x) / 2 *cos (7x -3x) /2 2 sin (7x + 3x) / 2

--------------------------- ===> -------------------------------------------------------- ====> -----------------------------------------

cos(7x) + cos(3x) 2 cos(7x + 3x) / 2 *cos (7x -3x) /2   2 cos(7x + 3x) / 2

sin ( 5 x )   

====> -------------------------------- ===> tan( 5x) option B

cos ( 5x )