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Irina-Kira [14]
2 years ago
8

Verify the identity.

1" title="cot (x-\frac{\pi }{2})=-tan" alt="cot (x-\frac{\pi }{2})=-tan" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
aleksley [76]2 years ago
7 0

Answer:

True

Step-by-step explanation:

assuming that you meant to write

cot (x-π//2) = - tan x

the identity is TRUE because,

- you can graph cot (x-π//2)  and  - tan x, and see that the graphs overlap

OR

-you solve for cot (x-π/2)

useful to know is that :

cot x=1/tan x, tan x = sin x/cos x,  

cos(x) =cos(-x), sin(-x) = -sin x,

cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = 1/tan (x-π/2) , yet tangent is sin x/cos x

cot (x-π/2) = cos (x-π/2) /sin (x-π/2) , factor -1

cot (x-π/2) = cos -(π/2-x) /sin -(π/2-x),  use facts: cos(x) =cos(-x), sin(-x) = -sin x

cot (x-π/2) = cos (π/2-x) / -sin (π/2-x), use cos(π/2 -x) =sin x, sin (π/2-x) =cos x

cot (x-π/2) = sin x / -cos x , again sin x /cos x = tan x

cot (x-π/2) = -tan x

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3 years ago
Which statements are true about the ordered pair (2, 3) and the system of equations?
mel-nik [20]

substitute the ordered pair (2, 3 )  into the 2 equations

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(2 × 2 ) - (2 × 3 ) = 4 - 6 = - 2 → False

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When (2, 3 ) is substituted into the first equation, the equation is true.

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8 0
3 years ago
What are the solutions to the equation 3x2 + 3x +7 = 0?​
KATRIN_1 [288]

Answer:

x is equal to 0.94 and -1.94

Step-by-step explanation:

3x² + 3x + 7 = 0

9x² + 9x + 21 = 0

9x² + 9x + 2.25 = 18.75

(3x + 1.5)² = 18.75

3x + 1.5 = ±√18.75

3x = -1.5  ±√18.75

x = (-1.5  ±√18.75) / 3

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7 0
3 years ago
the proper angle for a ladder is about 75 degrees. from the ground. suppose you have a 9 foot ladder. how far from the house sho
icang [17]

ANSWER:

2.33 foot

STEP-BY-STEP EXPLANATION:

We can calculate the distance from the staircase to the wall, by means of the trigonometric cosine ratio, which is the following:

\begin{gathered} \cos \theta=\frac{\text{ adjacent}}{\text{ hypotenuse}} \\ \theta=75\text{\degree} \\ \text{ hypotenuse = 9 foot} \\ \text{adjacent = x} \end{gathered}

Replacing and solving for x:

\begin{gathered} \cos 75=\frac{x}{9} \\ x=9\cdot\cos 75 \\ x=2.33 \end{gathered}

The distance would be 2.33 foot

3 0
1 year ago
What are the solutions of 2x^2 + 16x + 34 = 0?
nexus9112 [7]

Answer :

2x^2 + 16x + 34 = 0? X= -4 -1i X= 4+1i

Step-by-step explanation:

-

6 0
2 years ago
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