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3 years ago

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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