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Vitek1552 [10]
4 years ago
10

Simplify cotø(tanø+cotø)​

Mathematics
1 answer:
Sladkaya [172]4 years ago
4 0

Answer:

\large\boxed{\cot\theta(\tan\theta+\cot\theta)=1+\cot^2\theta=\dfrac{1}{\sin^2\theta}=\csc^2\theta}

Step-by-step explanation:

\text{Use}\\\\\text{distributive property:}\ a(b+c)=ab+ac\\\cot\alpha\tan\alpha=1.\\\\======================\\\\\cot\theta(\tan\theta+\cot\theta)=(\cot\theta)(\tan\theta)+(\cot\theta)(\cot\theta)\\\\=1+\cot^2\theta\\\\\text{If you want next transformation, then use:}\\\\\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\\\\\sin^2\alpha+\cos^2\alpha=1\\\\=======================

=1+\left(\dfrac{\cos\theta}{\sin\theta}\right)^2=1+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta}{\sin^2\theta}+\dfrac{\cos^2\theta}{\sin^2\theta}=\dfrac{\sin^2\theta+\cos^2\theta}{\sin^2\theta}\\\\=\dfrac{1}{\sin^2\theta}\\\\\text{If you want next transformation, then use:}\\\\\csc\alpha=\dfrac{1}{\sin\alpha}\\\\=\left(\dfrac{1}{\sin\theta}\right)^2=(\csc\theta)^2=\csc^2\theta

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How to solve<br><br> -3(x+4)=-15
egoroff_w [7]

Answer:

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Step-by-step explanation:

-3(x+4)=-15

---------------

-3         -3

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That should be right

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Explain how to evaluate (-9)(-6)(15)(-7+7) as simply as possible.
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Answer:

For this case we must explain how to simplify the following expression:

( -9)(-6)(15)(-7+7)

According to the PEMDAS algebraic resolution order method, operations within parentheses must be performed first.

So, we have:

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Different signs are subtracted and the major sign is placed.

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Rewriting the original expression we have:

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Every number multiplied by "0" results in "0".

Then, the expression is zero.

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3 years ago
The coordinates of the vertices of ΔDEF are D(2, 3), E(l, 1), and F(4, O).Find the coordinates for the image of ΔDEF after the t
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The translation <u>3 units to the right and 2 units down the plane</u> will result in the coordinates D' (-1, 1),E'(-2, -1) and F' (1, -2)

<h3>
Translation of coordinates</h3>

Translation is a transformation technique used to change the position of an object on an y-plane.

For instance translating a coordinate (x, y) into (x-3,y -2) means a shift of the image <u>3 units to the right and 2 units down the plane. In </u>order to get the corresponding coordinates, we will subtract 3 from the x-coordinates and 2 from the y-coordinates.

Given the coordinate of the triangle DEF as shown;

ΔDEF

D(2, 3),

E(l, 1), and;

F(4, O)

The translation <u>3 units to the right and 2 units down the plane</u> will result in the coordinates D' (-1, 1),E'(-2, -1) and F' (1, -2)

Learn more on translation here: brainly.com/question/12861087

#SPJ1

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