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I think trust on own self is first priority and trust on customer is second priority because if didn't trust own self you can't do good business and if you have no trust on customer than you can't carry your business for long time with anyone.
Rather than trust on customer or Own self. One should concentrate on imporving quality of prouct or service. Add some value in it. In turn, you will retain your customer, by which you will gain trust on your self as well as your product/service. Be more customer centric and try to gain the customer satisfaction. To Conclude, Customer Satisfaction will be the key here to get trust on own and customer.
At the outset you have to have trust on your self that you can deliver what customer expects from you and secondly you will have to trust customer that after fulfilling his requirement he is going to be with you as far as business is concerned.