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marysya [2.9K]
3 years ago
8

Simplify the expression tan(-x)csc(-x)/sec(-x)cot(-x)

Mathematics
2 answers:
erik [133]3 years ago
6 0
The answer is csc(x)cot(x)tan(x) over sec(x)

goldfiish [28.3K]3 years ago
5 0
\frac{ tan(-x) cosec (-x)}{sec (-x) cot (-x)} ≡ \frac{ [- tan(x)]  [-cosec (-x)]}{[sec (x)] [-cot (x)]}

                                 ≡ \frac{ tan(x) cosec (-x)}{-sec (x) cot (x)} 

                                 ≡ \frac{ (\frac{sin (x)}{cos (x)})   (\frac{1}{sin (x )}) }{(- \frac{1}{cos (x)}) ( \frac{cos (x)}{sin (x)})  }

                                 ≡ \frac{ \frac{1}{cos (x)} }{-  \frac{1}{sin (x)} }

                                 ≡ - \frac{sin (x)}{cos (x)}

                                 ≡ - tan (x)<span>
</span>
⇒ \frac{ tan(-x) cosec (-x)}{sec (-x) cot (-x)} ≡ tan (-x)

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\bf \stackrel{300~days}{\textit{Amount for Exponential Decay using Half-Life}} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &1\\ t=\textit{elapsed time}\dotfill &300\\ h=\textit{half-life}\dotfill &74 \end{cases} \\\\\\ A=1\left( \frac{1}{2} \right)^{\frac{300}{74}}\implies A=1\left( \frac{1}{2} \right)^{\frac{150}{37}}\implies \boxed{A\approx 0.060202}

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