What are the degrees of freedom associated with the factor(s) in this study design?

Mathematics

1 answer:

miss Akunina [59]2 years ago

3 0

Answer:

The question is unclear and incomplete.

Let me explain the degrees of freedom in statistics.

Step-by-step explanation:

Statistically, degrees of freedom which is denoted as DF is the number of independent values that can vary in an analysis without breaking any constraints. It can also be referred to as the number of independent values that a statistical analysis can estimate.

Degrees of freedom also define the probability distributions for the test statistics of various hypothesis tests.

The degree of freedom has the formula:

DF = N - 1 where N number of random variables

DF = (R - 1) x (C - 1) Where R is the number of data values and C is the number of groups

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Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$