已知cos(a+π⼀4)=3⼀5 sin2a⼀sin(π⼀4-a)

2025-01-31 12:58:23
推荐回答(1个)
回答1:

cos(a+π/4)=3/5
cosacosπ/4-sinasinπ/4 = 3/5
√2/2(cosa-sina) = 3/5
1/2(cosa-sina)^2 = 9/25
sin^2a+cos^2a-2sinacosa = 18/25
1-2sinacosa = 18/25
sinacosa=1/2(1-18/25)=7/50

sin2a/sin(π/4-a)
= 2sinacosa/cos{π/2-(π/4-a)}
= 2sinacosa/cos(a+π/4)
=2sinacosa/(3/5)
=10/3 sinacosa
= 10/3 * 7/50
= 7/15