It's Love Again (1936)

Elaine Bradford is a young singer and dancer, looking for her big break. Peter Carlton is a gossip columnist facing a deadline and a blank page. So, Peter invents "Mrs. Smythe-Smythe", a mysterious Englishwoman who spends her days hunting tigers in India, jumping out of airplanes, and generally driving men mad with her beauty. Since no one in London has ever seen Mrs. Smythe-Smythe, Elaine decides to impersonate the lady, in hopes that the publicity will land her the big break she's been looking for.