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2 years ago

13

Decide if it is always true or never true. x+1/2=x−1/2

2 answers:

Sergio039 [100]2 years ago

7 0

This is true because there is no value of x hope this helped

NNADVOKAT [17]2 years ago

4 0

ALWAYS TRUE

Step-by-step explanation:

Because there is no value of x

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Please help me!!!!!

Bas_tet [7]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the Sum & Difference Identity: tan (A - B) = (tanA - tanB)/(1 + tanA tanB)

Use the Half-Angle Identity: tan (A/2) = (1 - cosA)/(sinA)

Use the Unit Circle to evaluate tan (π/4) = 1

Use Pythagorean Identity: cos²A + sin²A = 1

<u>Proof LHS → RHS</u>

$\text{Given:}\qquad \qquad \qquad\dfrac{2\tan\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}{1+\tan^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)}$

$\text{Difference Identity:}\qquad \dfrac{2 \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{\tan\frac{\pi}{4}-\tan\frac{A}{2}}{1+\tan\frac{\pi}{4}\cdot \tan\frac{A}{2}}\bigg)^2}$

$\text{Substitute:}\qquad \qquad \dfrac{2 \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)}{1+ \bigg( \frac{1-\tan\frac{A}{2}}{1+\tan\frac{A}{2}}\bigg)^2}$

$\text{Simplify:}\qquad \qquad \qquad \dfrac{1-\tan^2\frac{A}{2}}{1+\tan^2\frac{A}{2}}$

$\text{Half-Angle Identity:}\qquad \quad \dfrac{1-(\frac{1-\cos A}{\sin A})^2}{1+(\frac{1-\cos A}{\sin A})^2}$

$\text{Simplify:}\qquad \qquad \dfrac{\sin^2 A-1+2\cos A-\cos^2 A}{\sin^2 A+1-2\cos A+\cos^2 A}$

$\text{Pythagorean Identity:}\qquad \qquad \dfrac{1-\cos^2 A-1+2\cos A}{2-2\cos A}$

$\text{Simplify:}\qquad \qquad \qquad \dfrac{2\cos A-2\cos^2 A}{2(1-\cos A)}\\\\.\qquad \qquad \qquad \qquad =\dfrac{2\cos A(1-\cos A)}{2(1-\cos A)}$

= cos A

LHS = RHS: cos A = cos A $\checkmark$

4 0

3 years ago

brantty works 21.5 hours every week . if she earns 8.50 per hour how much does she earn in one week round part a to the nearest

kari74 [83]

Step-by-step explanation:

1 hour - $8.50

21.5 hours (one week) - $8.50 × 21.5 = $182.75

One week = $183

8 0

2 years ago

Classify -42 in as many groups as possible on the Venn diagram.

Komok [63]

Answer:

B

Explanation:

-42 is a integer, but not irrational, and whole numbers are all positive except for 0.

4 0

2 years ago

Read 2 more answers

How much money should be deposited today in an account that earns 7% compounded semiannually so that it will accumulate to $12,0

Korvikt [17]

Given rate is = 7% or 0.07

Total amount needed = $12000

Time = 4 years

Here, the deposit is compounded semiannually, means twice per year and this gives 8 annual compounding periods in 4 years.

The equation becomes:

P= $\frac{12000}{(1+\frac{0.07}{2})^{2.4}}$

P = $\frac{12000}{1.035^{8}}$

Solving it, we get P = $ 9112.93

Hence $9112.93 should be deposited today.

3 0

3 years ago

What is the product?<br> (7x) (2x+5)(x2-4x-9)

3241004551 [841]

Answer:

=14x^2+35x

Step-by-step explanation:

8 0

3 years ago