Question

Please explain your answer. THX!

Answer 1

see explanation

Explanation:

(3)

Given cosΘ = -
`(4)/(5)`

Then by Pythagoras' theorem the third side is 3 ( 3,4, 5 triangle )

Since Θ in second quadrant then sinΘ > 0

sinΘ =
`(3)/(5)`

Using the trigonometric identity

sin2Θ = 2sinΘcosΘ, then

sin2Θ = 2 ×
`(3)/(5)` × -
`(4)/(5)` = -
`(24)/(25)`

(4)

Using the trigonometric identity

cos(x - y) = cosxcosy + sinxsiny

note cos15° = cos(45 - 30)°

cos(45 - 30) = cos45cos30 + sin45sin30

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

=
`\frac{\sqrt{2(√(3)+1) } }{4}`