Answer to Question #94289 in Trigonometry for Maxwell Danso-Abiam

Question

tan y =√2 , where x and y are acute angles, find the value of x if sin x = 1 - cos y

Answer 1

sin²y+cos²y=1; 1+tan²y=1/(cos²y); cos²y=1/(1+tan²y); cos y= (1/(1+tan²y))^1/2; cos y = 3^-1/2

sin x = 1 - 1/3^1/2= (3^1/2-1)/3^1/2; x = arcsin (3^1/2-1)/3^1/2

Using calculator x = 25 degrees