PLZ ANSWER QUICK WHAT IS THE RANGE OF THESE NUMBERS! WILL GIVE BRAINIEST

Prove that tan 10+tan 70'+taniou = tanio tanfo'tam 1oo.

Galina-37 [17]

Question:

Prove that:

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$

Answer:

Proved

Step-by-step explanation:

Given

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$

Required

Prove

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$

Subtract tan(10) from both sides

$- tan(10)+tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)$

$tan(70) + tan(100) = tan(10). tan(70). tan(100) - tan(10)$

Factorize the right hand size

$tan(70) + tan(100) = -tan(10)(-tan(70). tan(100) + 1)$

Rewrite as:

$tan(70) + tan(100) = -tan(10)(1-tan(70). tan(100))$

Divide both sides by $1-tan(70). tan(100)$

$\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = \frac{-tan(10)(1-tan(70). tan(100))}{1-tan(70). tan(100))}$

$\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10)$

In trigonometry:

$tan(A + B) = \frac{tan(A) + tan(B)}{1 - tan(A)tan(B)}$

So:

$\frac{tan(70) + tan(100)}{1 - tan(70)tan(100)}$ can be expressed as: $tan(70 + 100)$

$\frac{tan(70) + tan(100)}{1-tan(70). tan(100)} = -tan(10)$ gives

$tan(70 + 100) = -tan(10)$

$tan(170) = -tan(10)$

In trigonometry:

$tan(180 - \theta) = -tan(\theta)$

So:

$tan(180 - 10) = -tan(10)$

Because RHS = LHS

Then:

$tan(10) + tan(70) + tan(100) = tan(10). tan(70). tan(100)$ has been proven

6 0

3 years ago

you earn 10 points for every coin you collect in a video game. then you find a star that triples your score. write and simplify

Tomtit [17]

Answer:

The required expression for total number of points you earn is $P=10c+3p$ .

Step-by-step explanation:

Consider the provided information.

Let c represents the coin and p represents the points before getting star.

You earn 10 points for every coin you collect in a video game.

$p=10c$ ......(1)

You find a star that triples your score.

$star=3p$

Now the total number of points you earn is(P):

$P=10c+3p$

Substitute the value of p from equation 1.

$P=10c+3(10c)$

$P=40c$

5 0

4 years ago

Examine the equation and solution method shown below. Indentify the error and then solve the equation using a valid solution met

valkas [14]

3 ( 3x + 6 + x ) = 1

Step 1, apply distributive method.

9x + 18 + 3x = 1

Step 2, simplify the following

12x + 18 = 1

Step 3, Change side

12x = -17

Final answer

x = -17/12

The error/mistake was in step 2 where [ 9x +3x = 12x ]

Recheck the answer

3 ( 3x + 6 + x ) = 1

3 ( 3(-17/12) + 6 + -17/12 ) = 1

1 = 1

Hence proved our solution is correct.

5 0

3 years ago

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Write the equation of the line, in slope-intercept form, with the following information: slope: 1/3 y-intercept: (0, 2)

sp2606 [1]

Answer:

y=1/3x+2

Step-by-step explanation:

to put it in y=mx+b slope is m and b is the y intercept

6 0

3 years ago

Solve the equation for x. x2 = 9

NeX [460]

<h2>Solution :</h2>

= 2x = 9

= x = 9 ÷ 2 ( transposing ×2 from LHS to RHS changes ×2 to ÷2 )

= x = 4.5

Therefore , x = 4.5 .

5 0

4 years ago

Read 2 more answers