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已知cos(75°+α)=,α是第三象限角,求sin(195°-α)+cos(α...

已知cos(75°+α)=6ec8aac122bd4f6eα是第三象限角,求sin(195°-α)+cos(α-15°)的值.

 

- 【解析】∵cos(75°+α)=>0,α是第三象限角, ∴75°+α是第四象限角, 且sin(75°+α)=-=-. ∴sin(195°-α)+cos(α-15°) =sin[180°+(15°-α)]+cos(15°-α) =-sin(15°-α)+cos(15°-α) =-sin[90°-(75°+α)]+cos[90°-(75°+α)] =-cos(75°+α)+sin(75°+α) =--=-.
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