Question

若a∈(0,π/2)且sin^2 a+cos2a=1/4,求tan a的值

Answer 1

cos2a=cos^2a-sin^2a
即cos^2a=1/4,又a在第一象限，所以cosa=1/2
则tan a=根号3

Answer 2

sin²a+2cos²-1=1/4
sin²a+cos²a+cos²a=5/4
1+cos²a=5/4
cos²a=1/4
sec²a=4
1+tan²a=sec²a=4
tan²a=3
tana=√3