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Gemiola [76]
3 years ago
7

use the power-reducing formulas to rewrite the expression in terms of the first power of the cosine . . sin^6 x

Mathematics
1 answer:
andrey2020 [161]3 years ago
4 0
<span>1/128 (3 - 4 Cos[4 x] + Cos[8 x])</span>( sin^2(x) )^2 cos^4(x) 

<span>( (1 - cos^2(x) )^2 cos^4(x) </span>

<span>(1 - 2cos^2(x) + cos^4(x) ) cos^4(x) </span>

<span>cos^4(x) - 2cos^6(x) + cos^8(x) </span>

<span>( cos^2(x) )^2 - 2( cos^2(x) )^3 + ( cos^2(x) )^4 <==> knowing the identity; cos^2(x) = (1/2) * (1 + cos(2x)) </span>

<span>( (1/2) * (1 + cos(2x)) )^2 - 2( (1/2) * (1 + cos(2x)) )^3 + ( (1/2) * (1 + cos(2x)) )^4 </span>

( (1/4) * (1 + 2cos(2x) + cos^2(2x) )) - 2( (1/8) * (cos^3(2x) + 3cos^2(2x) + 3cos(2x) + 1) + ( (1/16) * cos^4(2x) + 4cos^3(2x) + 6cos^2(2x) + 4cos(2x) + 1) 
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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If we have 

y = 6x + 1 and x - y = 11, we can take advantage of  y - y = 0 as follows:
                                         Subtract x from both sides of the 2nd equation:
                                         -y = 11 - x

Now combine 

 y = 6x + 1
-y = 11 - x
--------------
0 = 5x + 12.  Solving for x, x = -12/5.     Using the equation above, find y:
                                                               -y = 11 - x
                                                                   = 11 - (-12/5)
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Then the solution is (-12.5, 67/5).

                      
3 0
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