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2 years ago

Sin^22x - 2cos2x + 2=0

Mathematics

1 answer:

zhuklara [117]2 years ago

5 0

Answer:

x=πn, n∈Z

Step-by-step explanation:

if sin²2x=1-cos²2x, then

1-cos²2x-2cos2x+2=0; ⇒ cos²2x+2cos2x-3=0; ⇔ (cos2x+3)(cos2x-1)=0;

$\left[\begin{array}{cc}cos2x+3=0\\cos2x-1=0\\\end{array} \ \ \left[\begin{array}{cc}x \ 'does-not-exist'\\cos2x=1\\\end{array} \ \ 2x=2\pi n, n=Z \ x=\pi n, n=Z$

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Given points A(-1, -2) and B(2, 4) where AP: BP=1:2, find the locus of point P.

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$x^2 + 4x + y^2 +8y = 0$

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Cross multiply

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Calculate AP and BP using the following distance formula:

$d = \sqrt{(x - x_1)^2 + (y - y_1)^2}$

So, we have:

$2 * \sqrt{(x - -1)^2 + (y - -2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

$2 * \sqrt{(x +1)^2 + (y +2)^2} = \sqrt{(x - 2)^2 + (y - 4)^2}$

Take square of both sides

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Evaluate all squares

$4 * [x^2 + 2x + 1 + y^2 +4y + 4] = x^2 - 4x + 4 + y^2 - 8y + 16$

Collect and evaluate like terms

$4 * [x^2 + 2x + y^2 +4y + 5] = x^2 - 4x + y^2 - 8y + 20$

Open brackets

$4x^2 + 8x + 4y^2 +16y + 20 = x^2 - 4x + y^2 - 8y + 20$

Collect like terms

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$3x^2 + 12x + 3y^2 +24y = 0$

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3 years ago

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stiks02 [169]

You need this key result: in any polygon, the sum of the interior angles is

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