Question

Tolong jawab beserta jalannya ya

Answer 1

Verified answer

1.) sin(90° - α) = ¾
➝ cos α = ¾
Ilustrasi segitiga
|\
|. \
|... \
|......\
| x.... \ 4
| .........\
| ...........\
| .............\
|______α\
........3

Maka x = √(4² - 3²)
= √(16 - 9)
= √7
= √7

sin α = √7 / 4
tan α = √7 / 3

cosec (180° + α) + tan (270° - α)
= -cosec α + cot α
= 2/√7 + 3/√7
= 5/√7
= 5√7 / 7

2.)
a. cos (270° + α) + cos (270° - α) + tan (270° + α)
= sin α - sin α - cot α
= -cot α

b. sin x + cos (3/2 π - x)
= sin x + cos (270° - x)
= sin x - sin x = 0

c. sin 45° sin 15° / cos 135° cos 105°
= ½(cos (45° - 15°) - cos (45° + 15°)) / ½(cos (135° - 105°) + cos (135° + 105°))
= (cos 30° - cos 60°) / (cos 30° + cos 240°)
= (½√3 - ½) / (½√3 - ½)
= 1