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pickupchik [31]
4 years ago
10

I need help proving this ASAP

Mathematics
1 answer:
Ket [755]4 years ago
6 0

Answer:

See explanation

Step-by-step explanation:

We want to show that:

\tan(x +  \frac{3\pi}{2} )  =  -   \cot \: x

One way is to use the basic double angle formula:

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{ \sin(x)  \cos( \frac{3\pi}{2} )  +   \cos(x)  \sin( \frac{3\pi}{2}) }{\cos(x)  \cos( \frac{3\pi}{2} )   -    \sin(x)  \sin( \frac{3\pi}{2}) }

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{ \sin(x) ( 0)  +   \cos(x) (  - 1) }{\cos(x) (0)   -    \sin(x) (  - 1) }

We simplify further to get:

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{ 0  -   \cos(x) }{0 +    \sin(x) }

We simplify again to get;

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  \frac{- \cos(x) }{ \sin(x) }

This finally gives:

\frac{ \sin(x +  \frac{3\pi}{2} ) }{\cos(x +  \frac{3\pi}{2} )}  =  -  \cot(x)

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Side of a rhombus is 5cm.if the lengthof one diagnol is 8cm,find the other
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Linda earns $600 each week working her full time job. Her employer has a 16% tax deduction on all monies earned each week
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3 years ago
Doug's garden produces 5.8 times as many vegetables as Kelsey's garden. Together, the gardens produce 102 pounds of vegetables.
muminat

Answer:

  • Doug's garden: 87 lbs
  • Kelsey's garden: 15 lbs

Step-by-step explanation:

Let k represent the pounds of produce coming from Kelsey's garden. Then Doug's garden produces 5.8k pounds of produce, and the total weight of it is ...

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3 0
3 years ago
What is the value of tan D?
Talja [164]
Hey there!

As according to the mathematical acronym SOH CAH TOA (Sin Opposite Hypotenuse, Cos Adjacent Hypotenuse, Tan Opposite Adjacent), the correct answer would be the first choice, \frac{12}{5}.

The reason behind this is because the tangent value of an angle is always the length value opposite of given angle over the value adjacent (or right next to) the given angle.

In this case, the question is asking for Tan D. The side value opposite of angle D would be 12, and the length value that is adjacent to angle D is 5.

Therefore, the value of tan D would be \frac{12}{5}.

Hope this helps and I hope you have a marvelous day! :)
5 0
3 years ago
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