The phrase 'strengthen the trust' is correct and can be used in written English.
You can use it when you want to express the idea that someone has worked to increase the trust between two people or groups of people. For example: "He did everything he could to strengthen the trust between the two countries".
"This initiative will on the whole strengthen the trust of citizens" in the business community, Mr. Putin said in his speech.
Chris Jennings, Mr. Clinton's health care adviser, said: "Dean is right that the Clinton Administration desired to constrain growth in the Medicare program and strengthen the trust fund.
In Merced, about 120 miles southeast of San Francisco, the Mercy hospital shaman program was designed to strengthen the trust between doctors and the Hmong community — a form of healing in the broadest sense.
Early in his testimony, he acknowledged that there was a "trust deficit" between the committee and the C.I.A. "If I am confirmed," he said, "I would make it my goal on day one of my tenure and every day thereafter to strengthen the trust between us".
"As the president of the United States and as the mayor of its largest city, the two pledged to work together to help strengthen the trust and bond between law enforcement and the local communities that they serve," White House press secretary Josh Earnest said.
Mr. Falise also tried to develop innovative ways to strengthen the trust's financial resources.
"Editorial control and compliance procedures in non-news areas of the BBC's Audio and Music department are inadequate and need to be strengthened," the trust said.
That strengthens the trust I have in our relationship.
Interviewees in both sites were confident that these engagement activities are effective ways of improving research literacy and strengthening the trust relationship between the host institutions and the community.
This review supports this relevance by identifying some of the factors of trust that motivate workers to willingly perform their duties and strengthen the bidirectional provider patient trust relationship.
Pressed by University of Pennsylvania professor Claire Finkelstein, Inglis strongly decried Snowden's leaks as illegal and morally illegitimate, but conceded that they have provided NSA with an opportunity "not only to restore trust in a system or a system of practices, but to go forward such that we strengthen the bonds of trust" with the public.
