Question

已知X为锐角，cos(π/4+x）= -3/5，求cosx的值

Answer 1

x为锐角
那么π/4+x∈(0,π)
cos(π/4+x）=-3/5
故sin(π/4+x)=√[1-(-3/5)^2]=4/5

所以cosx=cos[(π/4+x)-π/4]=cos(π/4+x)cos(π/4)+sin(π/4+x)sin(π/4)=(-3/5)*(√2/2)+(4/5)*(√2/2)=√2/10

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Answer 2

x为锐角，cos(π/4+x)= -3/5，sin(π/4+x)= 4/5
于是cosx=cos(π/4+x-π/4)=cos(π/4+x)cosπ/4+sin(π/4+x)sinπ/4
=(-3/5)*[(根号2)/2]+(4/5)*[(根号2)/2]
=(根号2)/10

Answer 3

因为：cos(π/4+x)=-3/5
所以sin(π/4+x)=4/5 .2个打开的：1.cosx-sinx=-3√2/5
2.cosx+sinx=√2/5
由1+2则可求解。得cosx=√2/10
从上面几种方法来看，我的较简便，望采纳