Question

Tolongin ya guys..Tentukan nilai dari :
a)sin 7,5° cos 7,5°
b)1-2 sin² 22,5
#Thanks buat yg mau bantu

Answer 1

•

cos 2a = 1 - 2 sin² a

•

1 - 2 sin² 22,5°

= cos 2(22,5°)

= cos 45°

= 1/2 √2

••

sin 2a = 2 sin a cos a

sin7,5° cos 7,5° = 1/2 sin 2(7,5°) = 1/2 sin 15°

cos 30° = 1 - 2 sin² 15°

1/2 √3 = 1 - 2 sin² 15°

2 sin² 15° = 1 - 1/2 √3

sin² 15° = (2 - √3)/4

sin 15° = 1/2 √(2 - √3)

•

sin7,5° cos 7,5°

= 1/2 sin 15°

= 1/4 √(2 - √3) ✔

Answer 2

Jawab:

trigonometri

sudut rangkap

Penjelasan dengan langkah-langkah:

a) sin 7,5 cos 7,5

= 1/2  (2 sin 7,5 cos 7,5)

= 1/2 sin 2(7,5)

= 1/2  sin 15

= 1/2  sin (45- 30)

= 1/2 { sin 45 cos 30 - cos 45  sin 30 }

= 1/2 { 1/2 √2 . 1/2 √3  - 1/2 √2 . 1/2}

= 1/2  { 1/4 √6 - 1/4 √2)

=  1/2 . 1/4 (√6 - √2)

= 1/8 (√6 - √2)

..

b) 1 - 2 sin² 22,5 =

= sin² 22.5 + cos² 22,5  - 2 sin² 22,5

= cos² 22,5 - sin² 22,5

= cos 2 (22,5)

= cos 45

= 1/2 √2