Question

Simplify the expression below. Make sure to reduce all fractions.

8sec(x)/-7csc(x)

Answer 1

16/7sin(2x)

Explanation:

-8×1/cos(x)×⅐×1/sin(x)

-8/7cos(x)sin(x)

-8/⁷/²×sin(2x)

-8/7sin(2x)/2

16/7sin(2x)

Answer 2

-
`(8)/(7)` tanx

Explanation:

Using the identities

secx =
`(1)/(cosx)` , cscx =
`(1)/(sinx)` , tanx =
`(sinx)/(cosx)`

Given

`(8secx)/(-7cscx)`

=
`((8)/(cosx) )/((-7)/(sinx) )` ← multiply numerator/ denominator by sinx

=
`(8(sinx)/(cosx) )/(-7)`

= -
`(8)/(7)` tanx