已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值!急!已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值急!化简:根号下(1-sin^2(440°))
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![已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值!急!已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值急!化简:根号下(1-sin^2(440°))](/uploads/image/z/1105126-70-6.jpg?t=%E5%B7%B2%E7%9F%A5sin%28%CF%80-a%29cos%28-8%CF%80-a%29%3D60%2F169%2C%E4%B8%94a%E2%88%88%28%CF%80%2F4%2C+%CF%80%2F2%29%2C%E6%B1%82sina%E4%B8%8Ecosa+%E7%9A%84%E5%80%BC%21%E6%80%A5%21%E5%B7%B2%E7%9F%A5sin%28%CF%80-a%29cos%28-8%CF%80-a%29%3D60%2F169%2C%E4%B8%94a%E2%88%88%28%CF%80%2F4%2C+%CF%80%2F2%29%2C%E6%B1%82sina%E4%B8%8Ecosa+%E7%9A%84%E5%80%BC%E6%80%A5%21%E5%8C%96%E7%AE%80%EF%BC%9A%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%881-sin%5E2%EF%BC%88440%C2%B0%EF%BC%89%EF%BC%89)
已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值!急!已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值急!化简:根号下(1-sin^2(440°))
已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值!急!
已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值
急!
化简:根号下(1-sin^2(440°))
已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值!急!已知sin(π-a)cos(-8π-a)=60/169,且a∈(π/4, π/2),求sina与cosa 的值急!化简:根号下(1-sin^2(440°))
有条件知sina>cosa>0
=>原式=sina*cosa=60/169
1=(sina)^2+(cosa)^2
=(sina+cosa)^2-2sina*cosa
=>(sina+cosa)^2=1+2sina*cosa
=1+120/169=289/169
=>sina+cosa=17/13
则sina,cosa可以看成一元二次方程的两个根
x^2-(17/13)x+(60/169)=0
解可得:x1=12/13,x2=5/13
=>sina=12/13
cosa=5/13
至于补充问题:
(sinx)^2+(cosx)^2=1
∴根号下(1-sin^2(440°))
=根号下(cos^2(440°))
=根号下(cos^2(80°))
=cos80°