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elena-s [515]
2 years ago
6

Sint/1-cost=cosect+cott

Mathematics
1 answer:
I am Lyosha [343]2 years ago
4 0
Start on the left side.<span><span><span>−<span>cot<span>(t)</span></span></span>+<span><span>sin<span>(t)</span></span><span>1<span>−<span>cos<span>(t)</span></span></span></span></span></span><span><span>-⁢<span>cott</span></span>+<span><span>sint</span><span>1<span>-⁢<span>cost</span></span></span></span></span></span>Multiply <span><span><span>sin<span>(t)</span></span><span>1<span>−<span>cos<span>(t)</span></span></span></span></span><span><span>sint</span><span>1<span>-⁢<span>cost</span></span></span></span></span> by <span><span><span>1+<span>cos<span>(t)</span></span></span><span>1+<span>cos<span>(t)</span></span></span></span><span><span>1+<span>cost</span></span><span>1+<span>cost</span></span></span></span>.<span><span><span>−<span>cot<span>(t)</span></span></span>+<span><span><span>sin<span>(t)</span></span><span>1<span>−<span>cos<span>(t)</span></span></span></span></span><span><span>1+<span>cos<span>(t)</span></span></span><span>1+<span>cos<span>(t)</span></span></span></span></span></span><span><span>-⁢<span>cott</span></span>+<span><span><span>sint</span><span>1<span>-⁢<span>cost</span></span></span></span>⁢<span><span>1+<span>cost</span></span><span>1+<span>cost</span></span></span></span></span></span>Combine.<span><span>−<span>cot<span>(t)</span></span></span>+<span><span><span>sin<span>(t)</span></span><span>(<span>1+<span>cos<span>(t)</span></span></span>)</span></span><span>(<span>1<span>−<span>cos(t</span></span></span></span></span></span>−<span><span>cot<span>(t)</span></span>+<span><span><span>sin<span>(t)</span></span>+<span><span>sin<span>(t)</span></span><span>cos<span>(t)</span></span></span></span><span><span>(<span>1<span>−<span>cos<span>(t)</span></span></span></span>)</span><span>(<span>1+<span>cos<span>(t)</span></span></span>)</span></span></span></span><span>-⁢<span>cott</span></span>+<span><span><span>sint</span>+<span><span>sint</span>⁢<span>cost</span></span></span><span><span>1<span>-⁢<span>cost</span></span></span>⁢<span>1+<span>cost</span></span></span></span><span><span>))</span><span>(<span>1+<span>cos<span>(t)</span></span></span>)</span></span>−
<span><span><span>cot<span>(t)</span></span>+<span><span><span>sin<span>(t)</span></span>+<span><span>sin<span>(t)</span></span><span>cos<span>(t)</span></span></span></span><span>1<span>−<span>cos2</span><span>(t)</span></span></span></span></span><span><span>-⁢<span>cott</span></span>+<span><span><span>sint</span>+<span><span>sint</span>⁢<span>cost</span></span></span><span>1<span>-⁢<span>cos2</span>t</span></span></span></span></span>Apply pythagorean identity.<span><span><span>−<span>cot<span>(t)</span></span></span>+<span><span><span>sin<span>(t)</span></span>+<span><span>sin<span>(t)</span></span><span>cos<span>(t)</span></span></span></span><span><span>sin2</span><span>(t)</span></span></span></span><span><span>-⁢<span>cott</span></span>+<span><span><span>sint</span>+<span><span>sint</span>⁢<span>cost</span></span></span><span><span>sin2</span>t</span></span></span></span>Write <span><span>cot<span>(t)</span></span><span>cott</span></span> in sines and cosines using the quotient identity.<span><span><span>−<span><span>cos<span>(t)</span></span><span>sin<span>(t)</span></span></span></span>+<span><span><span>sin<span>(t)</span></span>+<span><span>sin<span>(t)</span></span><span>cos<span>(t)</span></span></span></span><span><span>sin2</span><span>(t)</span></span></span></span><span><span>-⁢<span><span>cost</span><span>sint</span></span></span>+<span><span><span>sint</span>+<span><span>sint</span>⁢<span>cost</span></span></span><span><span>sin2</span>t</span></span></span></span>Simplify.1<span><span>sin<span>(t)</span></span><span>1<span>sint</span></span></span>Rewrite <span><span>1<span>sin<span>(t)</span></span></span><span>1<span>sint</span></span></span> as <span><span>csc<span>(t)</span></span><span>csct</span></span>.<span><span>csc<span>(t)</span></span><span>csct</span></span>Because the two sides have been shown to be equivalent, the equation is an identity.<span><span><span><span>−<span>cot<span>(t)</span></span></span>+<span><span>sin<span>(t)</span></span><span>1<span>−<span>cos<span>(t)</span></span></span></span></span></span>=<span>csc<span>(t)</span></span></span><span><span><span>-⁢<span>cott</span></span>+<span><span>sint</span><span>1<span>-⁢<span>cost</span></span></span></span></span>=<span>csct</span></span></span> is an <span>identity
</span>
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Answer:The first option has a higher cost per liter and the required cost is $1.40 per liter.

Step-by-step explanation:

Step-by-step explanation:  Given that a 2 liter bottle of juice cost $2.80. A box containing six 12 liter bottle sells for $3.90.

We are to select the option that has a higher cost per liter.

We will be using the UNITARY method to solve the given problem.

Option (1) :  

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Option (2) :  

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So, the cost of 1 liter bottle of juice will be

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Hopefully this helps- let me know if you have any questions!

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