Which expression is equivalent to sec2xcot2x?

a.
sin2x

b.
csc2x

c.
`(1)/(cos^2x)`

d.
`(1)/(tan^2x)`

B. csc²(x)

Step-by-step explanation:

You can use the relations ...

sec(x) = 1/cos(x)

csc(x) = 1/sin(x)

cot(x) = cos(x)/sin(x)

to replace the functions in your expression. Then you have ...

sec²(x)·cot²(x) = (1/cos(x)·cos(x)/sin(x))² = (1/sin(x))² = csc²(x)

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Alternate solution

You can also use the relation

cot(x) = csc(x)/sec(x)

Then ...

(sec(x)·cot(x))² = (sec(x)·csc(x)/sec(x))² = csc²(x)

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

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step-by-step explanation: