设sinX+sinY=1/4,cosX+cosY=1/3,求tan(X+Y)的值.要详解.
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设sinX+sinY=1/4,cosX+cosY=1/3,求tan(X+Y)的值.要详解.
利用和差化积公式:
sinX+sinY=2sin((X+Y)/2)cos((X-Y)/2)=1/4.(1)
cosX+cosY=2cos((X+Y)/2)cos((X-Y)/2)=1/3.(2)
(1)÷(2)得:
tan((X+Y)/2)=1/4*3=3/4
所以,利用倍角公式tan2α=2tanα/(1-tanαtanα)得
tan(X+Y)=tan(2((X+Y)/2))=(2*3/4)÷(1-(3/4)^2)=24/7
sinX+sinY=2sin((X+Y)/2)cos((X-Y)/2)=1/4.(1)
cosX+cosY=2cos((X+Y)/2)cos((X-Y)/2)=1/3.(2)
(1)÷(2)得:
tan((X+Y)/2)=1/4*3=3/4
所以,利用倍角公式tan2α=2tanα/(1-tanαtanα)得
tan(X+Y)=tan(2((X+Y)/2))=(2*3/4)÷(1-(3/4)^2)=24/7
设sinX+sinY=1/4,cosX+cosY=1/3,求tan(X+Y)的值.要详解.
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