Question

PLEASE HURRY 50PTS!!!!!!

Answer 1

cos 2θ =
`(17)/(145)`

Explanation:

given

tan θ =
`(8)/(9)` =
`(opposite)/(adjacent)`

these are the 2 legs of a right triangle

with opposite = 8 and adjacent = 9

let hypotenuse be h

using Pythagoras' identity in the right triangle

h² = 8² + 9² = 64 + 81 = 145 ( take square root of both sides )

h =
`√(145)`

then

sin θ =
`(opposite)/(hypotenuse)` =
`(8)/(√(145) )`

using the double angle formula

cos 2θ = 1 - 2sin²θ

= 1 - 2 (
`(8)/(√(145) )` )²

= 1 - 2 (
`(64)/(145)` )

= 1 -
`(128)/(145)`

=
`(145)/(145)` -
`(128)/(145)`

=
`(145-128)/(145)`

=
`(17)/(145)`