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Sunny_sXe [5.5K]
3 years ago
14

Solve the equation cot 2x + cot x =3

Mathematics
1 answer:
rusak2 [61]3 years ago
3 0

tan2x*cotx - 3 = 0

We know that: tan2x = sin2x/cos2x and cotx = cosx/sinx

==> sin2x/cos2x *cosx/sinx = 3

Now we know that sin2x = 2sinx*cosx

==> 2sinxcosx/cos2x * cosx/sinx = 3

Reduce sinx:

==> 2cos^2 x/ cos2x = 3

Now we know that cos2x = 2cos^2 x-1

==> 2cos^2 x/(2cos^2 x -1) = 3

==> 2cos^2 x = 3(2cos^2 x -1)

==> 2cos^2 x = 6cos^2 x - 3

==> -4cos^2 x= -3

==> 4cos^2 x = 3

==> cos^2 x = 3/4

==> cosx = +-sqrt3/ 2

<span>==> x = pi/6, 5pi/6, 7pi/6, and 11pi/6</span>

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Answer:

r=−5.3

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−7.4r−6.31=3.23−5.6r

−7.4r+−6.31=3.23+−5.6r

−7.4r−6.31=−5.6r+3.23

Step 2: Add 5.6r to both sides.

−7.4r−6.31+5.6r=−5.6r+3.23+5.6r

−1.8r−6.31=3.23

Step 3: Add 6.31 to both sides.

−1.8r−6.31+6.31=3.23+6.31

−1.8r=9.54

Step 4: Divide both sides by -1.8.

−1.8r/−1.8=9.54/−1.8

r=−5.3

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3 years ago
(x-y) (x-1,y+3) (I need the answer pls)
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Answer:

x² - 2xy + 3x + y² - 3y

Step-by-step explanation:

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X x(x - 1 y + 3) - y x (x - 1y + 3)

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Express a(2) (2a(-1/2)+a) in its simplest form
Soloha48 [4]
First lets simplify the first term and yield (2a)

The second term:
1.   2a * (-1/2) = -a
2.   -a + a = 0

Now we have simplified both terms to: (2a) (0)

Anything multiplied by 0 is 0, so the answer is also 0. 
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4 years ago
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Find the LCM of k^2 + 3k + 2 and 2k^2 + 14k + 20.
Airida [17]

Answer:

  C.  2(k +2)(k +5)(k +1)

Step-by-step explanation:

The LCM will be the product of unique factors.

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The unique factors are 2, (k+1), (k+2), (k+5), so the LCM is their product:

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