Recall that sin(π/2) = 1, and cos(π/2) = 0,

$\bf \textit{Sum and Difference Identities}
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sin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)
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sin(\alpha - \beta)=sin(\alpha)cos(\beta)- cos(\alpha)sin(\beta)
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cos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)
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cos(\alpha - \beta)= cos(\alpha)cos(\beta) + sin(\alpha)sin(\beta)\\\\
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$

$\bf tan\left(x+\frac{\pi }{2} \right)=-cot(x)\\\\
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tan\left(x+\frac{\pi }{2} \right)\implies \cfrac{sin\left(x+\frac{\pi }{2} \right)}{cos\left(x+\frac{\pi }{2} \right)}
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\cfrac{sin(x)cos\left(\frac{\pi }{2} \right)+cos(x)sin\left(\frac{\pi }{2} \right)}{cos(x)cos\left(\frac{\pi }{2} \right)-sin(x)sin\left(\frac{\pi }{2} \right)}\implies \cfrac{sin(x)\cdot 0~~+~~cos(x)\cdot 1}{cos(x)\cdot 0~~-~~sin(x)\cdot 1}
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\cfrac{cos(x)}{-sin(x)}\implies -cot(x)$

7 0

3 years ago

A rectangle has a perimeter of 22 feet. The width is 5 feet less than the length. Find the length and the width of the rectangle

Nata [24]

7 and 2 is the answer

6 0

3 years ago