若a属于0到90度,且cos2a+sin2a=1/4,求tana

若a属于0到90度,且cos2a+sin2a=1/4,求tana
若a属于0到90度,且cos2a+sin2a=1/4,求tana

若a属于0到90度,且cos2a+sin2a=1/4,求tana
cos2a+sin2a=1/4
√2(cos2acos45°+sin2asin45°)=1/4
cos(2a-45°)=√2/8
2a-45°=arccos(√2/8)=79.8°
2a=124.8°
a=62.4°
tana=1.913

cos2a+sin2a=1/4 即 (1﹣tan²a + 2tana) / (1+tan²a) = 1/4
=> 5 tan²a ﹣8 tana ﹣3 = 0
=> tana = (4+√31)/5 或 tana = (4﹣√31)/5
∵ 0∴ tana = (4+√31)/5