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PilotLPTM [1.2K]

3 years ago

13

Carlos bought an item online for $160 and he was charged $8 fee for shipping. What was the percent of the sale was the shipping

fee

1 answer:

prohojiy [21]3 years ago

6 0

Shipping charge was 5%

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Prove that sinxtanx=1/cosx - cosx

maks197457 [2]

Answer:

See below

Step-by-step explanation:

We want to prove that

$\sin(x)\tan(x) = \dfrac{1}{\cos(x)} - \cos(x), \forall x \in\mathbb{R}$

Taking the RHS, note

$\dfrac{1}{\cos(x)} - \cos(x) = \dfrac{1}{\cos(x)} - \dfrac{\cos(x) \cos(x)}{\cos(x)} = \dfrac{1-\cos^2(x)}{\cos(x)}$

Remember that

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Therefore,

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

Once

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Then,

$\dfrac{\sin(x)\sin(x)}{\cos(x)} = \sin(x)\tan(x)$

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