sin dx 15 sin( )  x x 1 (sin 15 sin 9 ) x x dx 1 1 1 = 2 1 = 1 30 cos 15 cos 9   x x c 18 Example 10 Find cos 5 cos 7 x xdx Solution cos 5 cos 7 x xdx = 1 2 cos 5 cos 7 x xdx = cos 1 12 cos( )dx  x x = cos dx 1 12 cos 2  x x 1 1 1 sin 12  2 x 2 12 = 1 1 sin 12 sin 2   x x c = 24 4 Example 11 Find sin 8 sin 15 x xdx Solution 1 2 sin 8 sin 15 x xdx sin 8 sin 15 x xdx = 1 = cos dx 2 23 cos( 7 )  x x 1 = (cos 23 cos 7 ) x x dx 47
1 sin 15 x  sin( x ) dx (sin 15 x sin 9 x ) dx = 1 2 1 1 = 1 30 cos 15 x  1 18 cos 9 x  c Example 10 Find cos 5 x cos 7 xdx Solution cos 5 x cos 7 xdx = = = 1 1 1 2 cos 5 x cos 7 xdx cos 12 x  cos( x )dx cos 12 x  cos 2 x dx = 1 1 2 12 sin 12 x  1 2 = 1 24 sin 12 x  1 4 sin 2 x  c Example 11 Find sin 8 x sin 15 xdx Solution sin 8 x sin 15 xdx = 1 2 sin 8 x sin 15 xdx = 1 2 cos 23 x  cos( 7 x ) dx = 1 (cos 23 x cos 7 x ) dx 47