(7)/(x-3)-(5)/(x+3)

1 answer:

3 0

As I look into the problem with a deeper meaning then math I realize this answer can be not as hard as it appears and it could be hard to answer it

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Verify identity: <br><br> (sec(x)-csc(x))/(sec(x)+csc(x))=(tan(x)-1)/(tan(x)+1)

Nikitich [7]

So hmmm let's do the left-hand-side first

$\bf \cfrac{sec(x)-csc(x)}{sec(x)+csc(x)}\implies \cfrac{\frac{1}{cos(x)}-\frac{1}{sin(x)}}{\frac{1}{cos(x)}+\frac{1}{sin(x)}}\implies 
\cfrac{\frac{sin(x)-cos(x)}{cos(x)sin(x)}}{\frac{sin(x)+cos(x)}{cos(x)sin(x)}}
\\\\\\
\cfrac{sin(x)-cos(x)}{cos(x)sin(x)}\cdot \cfrac{cos(x)sin(x)}{sin(x)+cos(x)}\implies \boxed{\cfrac{sin(x)-cos(x)}{sin(x)+cos(x)}}$

now, let's do the right-hand-side then

$\bf \cfrac{tan(x)-1}{tan(x)+1}\implies \cfrac{\frac{sin(x)}{cos(x)}-1}{\frac{sin(x)}{cos(x)}+1}\implies \cfrac{\frac{sin(x)-cos(x)}{cos(x)}}{\frac{sin(x)+cos(x)}{cos(x)}}
\\\\\\
\cfrac{sin(x)-cos(x)}{cos(x)}\cdot \cfrac{cos(x)}{sin(x)+cos(x)}\implies \boxed{\cfrac{sin(x)-cos(x)}{sin(x)+cos(x)}}$

7 0

2 years ago

A man bought a lot for 1200 and sold it for 1500. his percent of gain based on his purchase was

jok3333 [9.3K]

Answer: The percent gain was 25%.

Step-by-step explanation:

Given, Cost price of lot = $1,200

Selling price of lot = $1,500

The percent gain = $\dfrac{\text{selling price- cost price}}{\text{cost price}}\times100$

⇒ Percent gain = $\dfrac{1500-1200}{1200}\times100\%$

$\Rightarrow\text{ Percent gain}=\dfrac{300}{1200}\times100\%\\\\\Rightarrow\text{ Percent gain}=\dfrac{1}{4}\times100\%\\\\\Rightarrow\text{ Percent gain}=25\%$