不难的1:a、b为锐角,且满足sina=√5/5cosb=√10/10则a+b为多少2:设0

Question

不难的
1:a、b为锐角,且满足sina=√5/5 cosb=√10/10 则a+b为多少
2:设0

Answer 1

1:a、b为锐角,且满足sina=√5/5 cosb=√10/10 则a+b为多少
0 < a < π/2,
0 < b < π/2,
0 < cosa = [1-(sina)^2]^(1/2) = 2/5^(1/2)
0 < sinb = [1-(cosb)^2]^(1/2) = 3/(10)^(1/2)
0 < a + b < π
cos(a+b) = cosacosb - sinasinb = 2/5^(1/2)*1/(10)^(1/2) - 1/5^(1/2)*3/(10)^(1/2)
= -1/(50)^(1/2) = -2^(1/2)/10 < 0.
a+b = π - arccos[2^(1/2)/10]
2:设0