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2 years ago

Prove the trig identity cosec theta / cot theta + tan theta = cos theta

Mathematics

1 answer:

Agata [3.3K]2 years ago

5 0

See attached images for proof.

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For the matrices below. Find all (real) eigenvalues. <br><br> A= [7 9]<br> [0 9]

Jet001 [13]

Answer:

The answer is "9 and 7".

Step-by-step explanation:

Given:

$A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right]$

Using formula:

$|A-\lambda \cdot I|= 0\\\\$

$\to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\$

$\to \lambda=7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda=9\\\\$

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3 years ago

What is 2/4 + 4/5 - 7/10 ? Please help

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Make sure they have all common denominators
$\frac{2}{4} + \frac{4}{5} - \frac{7}{10}$

$\frac{2}{4} * \frac{5}{5} = \frac{10}{20}$

$\frac{4}{5} * \frac{4}{4} = \frac{16}{20}$

$\frac{7}{10} * \frac{2}{2} = \frac{14}{20}$

$\frac{10}{20} + \frac{16}{20} - \frac{14}{20}$

Add $\frac{10}{20} + \frac{16}{20} = \frac{26}{20}$
$\frac{26}{20} - \frac{14}{20} = \frac{12}{20}$

To simplify, you must find the largest common factor which 4
In $\frac{12}{20}$
12÷4=3 and 20÷4=5

The answer is $\frac{3}{5}$

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3 years ago

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