There are countless examples of companies who have spent a lot of time, money, and effort to make their branding the best it can be, only for it to collapse in an instant due to losing the trust of consumers. Without trust, they have no customers, and without customers, there is no business.
The first area you can ensure your brand is seen as trustworthy comes not from your marketing or advertising but in your day-to-day dealings with your customers. It beggars belief that a company will spend a fortune on developing and marketing a product, but then scrimp on its customer service. Nothing kills the trust in your business and its brand quicker than not looking after customers once they have bought your product or service.