Question

已知a是锐角且cos^4a-sin^4a=3/5,求(sin^2a+3sinacosa-cos^2a)/(2sin^2a

Answer 1

cos^4a-sin^4a=3/5

(cos²a-sin²a)( cos²a+sin²a)=3/5

因为 cos²a+sin²a=1

所以cos²a-sin²a=3/5

cos²a=4/5,sin²a=1/5

cos²a*sin²a=4/25

a是锐角cosa*sina=2/5

所以(sin²a+3sinacosa-cos²a)/(2sin²a+cos²a)

=(1/5+6/5-4/5)/(2/5+4/5)=1/2