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Hitung nilai dari: sin 4 5 π ​ ⋅ tan 4 7 π ​ − ( cos 9 π ) 2

Hitung nilai dari:  

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S. Nur

Master Teacher

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Ingat: 1. 2. 3. 4. Jadi

Ingat:

1. begin mathsize 14px style sin space open parentheses straight pi plus straight x close parentheses equals negative sin space x end style

2. begin mathsize 14px style tan space open parentheses 2 straight pi minus straight x close parentheses equals negative tan space x end style

3. begin mathsize 14px style cos space left parenthesis k times 2 straight pi space plus space straight x right parenthesis equals cos space straight x end style

4. begin mathsize 14px style cos space left parenthesis straight pi minus straight x right parenthesis equals negative cos space x end style

Jadi

begin mathsize 14px style sin space fraction numerator 5 straight pi over denominator 4 end fraction times tan fraction numerator 7 straight pi over denominator 4 end fraction minus left parenthesis cos space 9 straight pi right parenthesis squared space equals sin space open parentheses straight pi plus straight pi over 4 space close parentheses times space tan space open parentheses 2 straight pi minus straight pi over 4 close parentheses minus left parenthesis cos space left parenthesis 4 times 2 straight pi plus straight pi right parenthesis right parenthesis squared space equals open parentheses negative sin space straight pi over 4 close parentheses space times space open parentheses negative tan space straight pi over 4 close parentheses minus left parenthesis cos space straight pi right parenthesis squared space equals open parentheses negative 1 half square root of 2 close parentheses space times space left parenthesis negative 1 right parenthesis minus left parenthesis cos space left parenthesis straight pi minus 0 to the power of ring operator right parenthesis right parenthesis squared space equals 1 half square root of 2 minus left parenthesis negative cos space 0 to the power of ring operator right parenthesis squared space equals 1 half square root of 2 minus left parenthesis negative 1 right parenthesis squared space equals 1 half square root of 2 minus 1 end style

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