Question 885143
To prove:
cos^2 (tan inverse 2) + sin^2 (cot inverse 3)= 3/10
let x=angle whose tan=2
let y=angle whose cot=3
..
tan(x)=2
hypotenuse of working right triangle=√(2^2+1^2)=√(4+1)=√5
cos(x)=1/√5
cos^2(x)=1/5
..
cot(y)=3
tan(y)=1/cot(y)=1/3
hypotenuse of working right triangle=√(1^2+3^2)=√(1+9)=√10
sin(y)=1/√10
sin^2(y)=1/10
..
cos^2 (tan inverse 2) + sin^2 (cot inverse 3)=1/5+1/10=3/10
verified: left side =right side