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

Hitung nilai dari: $sin \frac{5 π}{4} \cdot tan \frac{7 π}{4} - (cos 9 π)^{2}$

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