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3 years ago

For this item, enter the answer in the space provided.

Mathematics

1 answer:

Tanya [424]3 years ago

7 0

Answer:

Step-by-step explanation:

0.092

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<img src="https://tex.z-dn.net/?f=prove%20that%5C%20%20%5Ctextless%20%5C%20br%20%2F%5C%20%20%5Ctextgreater%20%5C%20%5Cfrac%20%7B

inysia [295]

$\large \bigstar \frak{ } \large\underline{\sf{Solution-}}$

Consider, LHS

$\begin{gathered}\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {sec}^{2}x - {tan}^{2}x = 1 \: \: }} \\ \end{gathered} \\ \\ \text{So, using this identity, we get} \\ \\ \begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - ( {sec}^{2}\theta - {tan}^{2}\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

We know,

$\begin{gathered}\boxed{\sf{ \:\rm \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: \: }} \\ \end{gathered} \\$

So, using this identity, we get

$\begin{gathered}\rm \: = \:\dfrac { \tan \theta + \sec \theta - (sec\theta + tan\theta )(sec\theta - tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered}$

can be rewritten as

$\begin{gathered}\rm\:=\:\dfrac {(\sec \theta + tan\theta ) - (sec\theta + tan\theta )(sec\theta -tan\theta )} { \tan \theta - \sec \theta + 1 } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac {(\sec \theta + tan\theta ) \: \cancel{(1 - sec\theta + tan\theta )}} { \cancel{ \tan \theta - \sec \theta + 1} } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:sec\theta + tan\theta \\\end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1}{cos\theta } + \dfrac{sin\theta }{cos\theta } \\ \end{gathered} \\ \\ \\\begin{gathered}\rm \: = \:\dfrac{1 + sin\theta }{cos\theta } \\ \end{gathered}$

<h2>Hence,</h2>

$\begin{gathered} \\ \rm\implies \:\boxed{\sf{ \:\rm \: \dfrac { \tan \theta + \sec \theta - 1 } { \tan \theta - \sec \theta + 1 } = \:\dfrac{1 + sin\theta }{cos\theta } \: \: }} \\ \\ \end{gathered}$

$\rule{190pt}{2pt}$

5 0

2 years ago

Fill in the blank.

3241004551 [841]

<span>The vertical asymptotes of the function cosecant are determined by the points that are not in the domain.</span>

8 0

3 years ago

Read 2 more answers

L=3cm×b=4cm×h=2cm <br>Can u pls help

Makovka662 [10]

Answer:

24 cm or h= 1/2 cm , b= 1 1/3 cm, l = 3cm

Step-by-step explanation:

3 x 4 x 2 = 12

6 0

3 years ago

Find an explicit formula for f(n).

soldi70 [24.7K]

Answer:

f(n) = 2n - 2

Step-by-step explanation:

Given the recursive formula

f(n) = f(n - 1) + 2 with f(1) = 0, then

f(2) = f(1) + 2 = 0 + 2 = 2

f(3) = f(2) + 2 = 2 + 2 = 4

f(4) = f(3) + 2 = 4 + 2 = 6

The terms of the sequence are 0, 2, 4, 6, ....

These are the first 4 terms of an arithmetic sequence with explicit formula

f(n) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here d = 2 - 0 = 4 - 2 = 6 - 4 = 2 and a₁ = 0, thus

f(n) = 0 + 2(n - 1), that is

f(n) = 2n - 2 ← explicit formula

5 0

3 years ago

Earlier we investigated the relationship between x = payroll (in millions of dollars) and y = number of wins for Major League Ba

Minchanka [31]

Answer:

Kindly check explanation

Step-by-step explanation:

Given that:

Equation of regression line : y^ = 60.7 + 0.139x

x = payroll (in millions of dollars) and y = number of wins for Major League Baseball teams in 2016.

From the general regression equation:

y = mx + c

Where m = slope of regression line.

The slope (m) of the equation given is 0.139

The slope could be interpreted as ; for every per unit change in y (every win a major league baseball team has in 2016), the payroll in million dollar increases by a product of 0.139

4 0

3 years ago