1-Verify the identity. sin 3x + cos 3x cot 3x = csc 3x sin 3x + cos 3x sin 3x + cos 3x cot 3x = sin 3x = + cos2 3x sin 3x 1 = = csc 3x 2-Verify the identity. sec2 3u 1 sec2 3u = sin2 3u 1 sec2 3u 1 =1sec2 3u =1- = sin2 3u 3-Verify the identity. tan2 sin2 = tan2 sin2 tan2 sin2 = cos2 sin 2 = 1 cos2 1 (sec2 1) = = tan2 sin2 4-Verify the identity. cot tan sin + cos = csc sec cot tan sin + = cos sin cos sin + cos cos2 = sin cos sin + cos (cos + sin ) = sin cos (sin + cos ) cos sin cos = = csc sec 5-Verify the identity. tan2 2x sec 2x + 1 = 1 cos 2 x cos 2x tan2 2x sec 2x + 1 = 1 sec 2x + 1 (sec 2x + 1) = sec 2x + 1 = 1 1 = 1 = 1 cos 2 x cos 2x 6-Verify the identity. (sin2 + cos2 )10 = 1 (sin2 + cos2 )10 = 10 = 1 7-Verify the identity. sin cos + cos sin cos cos sin sin = tan + tan 1 tan tan Here we will begin with the right hand side of the identity. sin cos + cos sin cos cos tan + tan 1 tan tan = cos cos sin cos + cos sin = cos cos sin sin 8-Verify the identity. tan 3 1+ sec 3 + 1+ sec 3 tan 3 = 2 csc 3 tan2 3 + tan 3 1+ sec 3 + = 1+ sec 3 tan 3 2 (1 + sec 3)tan 3 (sec2 3 1) + 1 + 2 sec 3 + = (1 + sec 3)tan 3 = 2 sec 3 sec 3 + 1 (1 + sec 3) 2 cos 3 = sin 3 = 2 csc 3 9-Verify the identity. sin3 2t + cos3 2t = (1 sin 2t cos 2t)(sin 2t + cos 2t) sin 2t + sin3 2t + cos3 2t = sin2 2t + cos2 2t = (1 sin 2t cos 2t)(sin 2t + cos 2t) 10-Verify the identity. cot(3t) + tan(3t) cot 3t = sec2 3t cot 3t cot(3t) + tan(3t) = cot 3t cot 3t 1 = cot 3t 1+ = = sec2 3t 11-Verify the identity. ln cot 4x = ln tan 4x ln = ln cot 4x 1 = ln tan 4x 12-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) cos 2x 19 =0 x= 13-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) cot2 3 cot = 0 = 14-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) tan2 x sin x = 3 sin x x= 15-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) sin x + cos x = 0 x= 16-comma-separated list. If there is no solution, enter NO SOLUTION.) sin2 + 2 sin 8 = 0 = 17-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 2 tan t sec2 t = 0 t= 18-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) csc5 = 4 csc = 19-Find the solutions of the equation that are in the interval [0, 2 ). (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) 2 cos v sec v sec v = 4 cos v 2 v=