Help me on 4 please and thank u

Verify that each equation is an identity (1 - sin^(2)((x)/(2)))/(1+sin^(2)((x)/(2)))= (1+cosx)/(3-cosX)

Allisa [31]

Answer:

Given that we have;

$sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }$

By the application of the law of indices and algebraic process of adding a and subtracting a fraction from a whole number, we have;

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

Step-by-step explanation:

An identity is a valid or true equation for all variable values

The given equation is presented as follows;

$\dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

From trigonometric identities, we have;

$sin \left (\dfrac{x}{2} \right ) = \sqrt{\dfrac{1 - cos (x)}{2} }$

$\therefore sin^2 \left (\dfrac{x}{2} \right ) = \dfrac{1 - cos (x)}{2}$

$1 - sin^2 \left (\dfrac{x}{2} \right ) = 1 - \dfrac{1 - cos (x)}{2} = \dfrac{2 - (1 - cos (x))}{2} = \dfrac{1 + cos (x))}{2}$

$1 + sin^2 \left (\dfrac{x}{2} \right ) = 1 + \dfrac{1 - cos (x)}{2} = \dfrac{2 + 1 - cos (x))}{2} = \dfrac{3 - cos (x))}{2}$

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( \dfrac{1 + cos (x)}{2} \right)}{\left (\dfrac{3 - cos (x)}{2} \right ) } =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

$\therefore \dfrac{\left ( 1 - sin^2 \left (\dfrac{x}{2} \right ) \right )}{\left ( 1 + sin^2 \left (\dfrac{x}{2} \right ) \right )} =\dfrac{\left ( 1 + cos (x))}{(3 - cos (x))}$

3 0

3 years ago

1. (4y^3)^3

IRINA_888 [86]

1. 64y^9
2.256u^12v^4
3.8a^3b^4 * b^4
4. vu^4 * 8vu^6

6 0

4 years ago

Solve for x<br>x/6 + ≥ −2

Verizon [17]

There is no answer because you didn’t put some thing after the + so it wouldn’t show nothing

3 0

3 years ago

Its r9ght here just look at ut

Cloud [144]

Answer:

its 400 . 1200 divided by 3 in 400.

Step-by-step explanation:

3 0

3 years ago

Ayesha works as a real estate agent. Her annual gross salary is $28,000. From this, she must pay 20% income tax on anything earn

Lady bird [3.3K]

Answer:

Step-by-step explanation:

Annual gross salary = $28000

Income tax = 20% on anything above $15000

So she's taxable for $5000

Rent loan = $140 per month = $140 * 12= $1680 per annum

Tax deductible per annum = 20% of $5000

20 / 100 * $5000 = $1000

Total amount she takes home per annum =

Gross salary per annum - tax - loan =

($28000 - $1000 - $1680) = $25,320

Ayesha takes home $25,320 home annually.

8 0

4 years ago