Question

Tolong dibantu nomor 2 kak

Answer 1

No 2)

a. 4 sin π/8.cos 7π/24

Berarti

2(2.sin π/8.cos 7π/24) =

2(2.sin 22,5°.cos 52,5°) =

2(sin(22,5+52,5) + (sin(22,5-52,5) =

2(sin 75 + sin (-75) =

2(sin (30+45) + (-sin(30+45)) =

2(sin 30.cos 45 + cos 30.sin 45) + (-(sin 30 cos 45 + cos 30 sib 45)) =

2(1/2.1/2√2 + 1/2√3.1/2√2) -(1/2.1/2√2 + 1/2√3/.1/2√2)) =

2

b )

cos 75 = cos (30+45) = cos 30 cos 45 - sin 30 sin 45=1/2√3 .1/1√2 - 1/2 . 1/2√2 = 1/4√6 -1/4√2

Cos 105 = cos (60+45) = cos 60.cos 45 - sin 60 sin 45 = 1/2.1/2√2 - 1/2√3/.1/2√2 =

(1/4)√2 - (1/4)√6

Jadi cos 75.cos 105 = (1/4√6-1/4√2) (1/4√2 - 1/4√6) = (1/16)√12 -(1/16).6 - (1/16).2 +(1/16)√12 = (2/16).2√3 -(3/8) -(1/8) + (2/16).2√3 =

(1/4)√3 + (1/4)√3 - 1/2 =

1/2√3 - 1/2 =

1/2(√3-1)

Oke ??