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4 years ago

Simplify the expression

Mathematics

1 answer:

chubhunter [2.5K]4 years ago

4 0

Answer:

sin(α) -cos(α)

Step-by-step explanation:

$\dfrac{2\sin^2{\alpha}-1}{\sin{\alpha}+\cos{\alpha}}=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{(\sin{\alpha}+\cos{\alpha})(\sin{\alpha}-\cos{\alpha})}\\\\=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{\sin^2{\alpha}-\cos^2{\alpha}}=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{\sin^2{\alpha}-(1-\sin^2{\alpha})}\\\\=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{2\sin^2{\alpha}-1}\\\\=\sin{\alpha}-\cos{\alpha}$

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Answer:

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Using the second column, we can see that the total number of students that do not have a part time job is 18+24=42.

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