Prove the identity using the following rules, Algebra, reciprocal, quotient, Pythagorean, and odd/even?

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Prove the identity using the following rules, Algebra, reciprocal, quotient, Pythagorean, and odd/even?

$\frac{csc (- x)}{sec (- x)} + \frac{cos (- x)}{sin (- x)} = - 2 cot x$ $csc(-x)/sec(-x)+cos(-x)/sin(-x)=-2cotx$

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Answer 1 · 2018-04-21T20:31:59

check the explanation below

Explanation:

$\frac{csc (- x)}{sec (- x)} = \frac{\frac{1}{sin (- x)}}{\frac{1}{cos (- x)}} = \frac{cos (- x)}{sin (- x)}$ $csc(-x)/sec(-x)=(1/sin(-x))/(1/cos(-x))=cos(-x)/sin(-x)$ $\to reciprocal$ $color(green)(rarr "reciprocal"$

now substitute

$\frac{cos (- x)}{sin (- x)} + \frac{cos (- x)}{sin (- x)} = 2 \frac{cos (- x)}{sin (- x)}$ $cos(-x)/sin(-x)+cos(-x)/sin(-x)=2cos(-x)/sin(-x)$

$sin x is odd so sin (- x) = - sin x$ $color(blue)(sinx " is odd so "sin(-x)=-sinx"$

$cos x is even so cos (- x) = cos x$ $color(blue)( cosx " is even so "cos(-x)=cosx$

Substitute

$= 2 \frac{cos x}{- sin x}$ $=2cosx/-sinx$ $\to e v e n and o d d functions$ $color(green)(rarreven and odd " functions"$

$= - 2 cot (x)$ $=-2cot(x)$ $\to q u o i t e n t$ $color(green)(rarrquoitent$

I hope this was helpful.

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Prove the identity using the following rules, Algebra, reciprocal, quotient, Pythagorean, and odd/even?

$\frac{csc (- x)}{sec (- x)} + \frac{cos (- x)}{sin (- x)} = - 2 cot x$ $csc(-x)/sec(-x)+cos(-x)/sin(-x)=-2cotx$

1 Answer

Explanation:

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Science

Math

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Prove the identity using the following rules, Algebra, reciprocal, quotient, Pythagorean, and odd/even?

csc(−x)sec(−x)+cos(−x)sin(−x)=−2cotxcsc(-x)/sec(-x)+cos(-x)/sin(-x)=-2cotx

1 Answer

Explanation:

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Impact of this question

$\frac{csc (- x)}{sec (- x)} + \frac{cos (- x)}{sin (- x)} = - 2 cot x$ $csc(-x)/sec(-x)+cos(-x)/sin(-x)=-2cotx$