Toán Lớp 11: xét tính chẵn lẻ f(x)= sin^5(3x).cos(3pi-7x)
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Toán Lớp 11: xét tính chẵn lẻ f(x)= sin^5(3x).cos(3pi-7x)
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f\left( x \right) = {\sin ^5}3x\cos \left( {3\pi – 7x} \right) = {\sin ^5}3x\cos \left( {\pi – 7x} \right)\\
= – {\sin ^5}3x\cos 7x\\
f\left( { – x} \right) = {\sin ^5}\left( { – 3x} \right)\cos \left( {3\pi – 7\left( { – x} \right)} \right)\\
= – {\sin ^5}3x\cos \left( {3\pi + 7x} \right)\\
= – {\sin ^5}3x\cos \left( {7x + \pi } \right)\\
= – {\sin ^5}3x – \left( {\cos 7x} \right)\\
= {\sin ^5}3x.\cos 7x = – f\left( x \right)
\end{array}$
f\left( x \right) = {\sin ^5}3x.\cos \left( {3\pi – 7x} \right)\\
= {\sin ^5}3x.\cos \left( {\pi – 7x} \right)\\
= {\sin ^5}3x.\left( { – \cos 7x} \right)\\
= – {\sin ^5}3x.\cos 7x\\
f\left( { – x} \right) = – {\sin ^5}\left( { – 3x} \right).\cos \left( { – 7x} \right)\\
= {\sin ^5}3x.\cos \left( {7x} \right) = – f\left( x \right)\\
\to lẻ
\end{array}\)