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ExtremeBDS [4]
3 years ago
12

Prove the identity

Mathematics
1 answer:
Troyanec [42]3 years ago
3 0

Answer:

Proved

Step-by-step explanation:

The options are not given. So, I will solve from scratch

Given

\frac{secx-1}{tan x}= \frac{tanx}{secx+1}

Required

Prove

Multiply the right-hand side by \frac{secx + 1}{secx + 1}

\frac{secx-1}{tan x} * \frac{secx + 1}{secx + 1}= \frac{tanx}{secx+1}

Apply difference of two squares on the numerator

\frac{sec^2 x - 1}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}

In trigonometry:

tan^2x = sec^2x - 1

So, we have:

\frac{tan^2 x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}

\frac{tan x * tan x}{(tanx)(secx + 1)} =\frac{tanx}{secx+1}

tan x cancels out

\frac{tan x}{secx + 1} =\frac{tanx}{secx+1}

<em>Proved</em>

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Answer:

60 minutes for the larger hose to fill the swimming pool by itself

Step-by-step explanation:

It is given that,

Working together, it takes two different sized hoses 20 minutes to fill a small swimming pool.

takes 30 minutes for the larger hose to fill the swimming pool by itself

Let x be the efficiency to fill the swimming pool by larger hose

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<u>To find LCM of 20 and 30</u>

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<u>To find the efficiency </u>

Let x be the efficiency to fill the swimming pool by larger hose

and y be the efficiency to fill the swimming pool by larger hose

x = 60/30 =2

x + y = 60 /20 = 3

Therefore efficiency of y = (x + y) - x =3 - 2 = 1

so, time taken to fill the swimming pool by small hose = 60/1 = 60 minutes

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3 years ago
What lowest terms 19/31
jonny [76]
The lowest terms for 19/31 would be 1
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6 + 23(3)

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Step-by-step explanation:

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Merina is scheduled to make two loan payments to Bradford in the amount of $1,000 each, two months and nine months from now. Mer
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\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{8.5\% of 2000}}{\left( \cfrac{8.5}{100} \right)2000}\implies 170 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\stackrel{principal}{2000}~~ + ~~\stackrel{interest}{170}}{2}\implies \stackrel{\textit{two equal payments of}}{1085}

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1 year ago
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