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Answer is T = 1728 N. 
First do a free body diagram with the center being the middle of the rope. The free body diagram shud include two tensions acting away from the center on the left and right side of the center and each form an angle that is 10 degrees to the horizontal. Then a force acting downward which represents the weight of the acrobat, must also be incorporated. 
Then using statics determine the equation for the summation the forces in the y or vertical direction: 
You shud get: Fy = 0 = Tsin10 + Tsin10 - 600 
-----> 2Tsin10 = 600 
-----> T = 1728 N. 
There you go! Gud luck with you.