Question

I need help figuring out what I did wrong

Answer 1

d

Explanation:

Answer 2

D

Explanation:

Using the addition formula for sine

sin(a + b) = sinacosb + cosasinb

and the exact values

sin(
`(\pi )/(4)` ) = cos(
`(\pi )/(4)` ) =
`(√(2) )/(2)` , cos(
`(\pi )/(6)`) =
`(√(3) )/(2)` , sin(
`(\pi )/(6)`) =
`(1)/(2)`

Note that
`(5\pi )/(12)` =
`(\pi )/(4)` +
`(\pi )/(6)` , thus

sin(
`(5\pi )/(12)`)

= sin(
`(\pi )/(4)` +
`(\pi )/(6)` )

= sin(
`(\pi )/(4)`)cos(
`(\pi )/(6)` ) + cos(
`(\pi )/(4)`)sin(
`(\pi )/(6)`)

= (
`(√(2) )/(2)` ×
`(√(3) )/(2)` ) + (
`(√(2) )/(2)` ×
`(1)/(2)` )

=
`(√(6) )/(4)` +
`(√(2) )/(4)`

=
`(√(6)+√(2) )/(4)` → D