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Matematika SMA
Trigonometri

Pembahasan :
1||

a. Sin 60 . Cos 30 + Cos 60 . Sin 30
= Sin (60 + 30)
= Sin 90
= 1

b. 2(tan 45°)² + Cos 30° - (Sin 60)²
= 2(1)² + (1/2 √3) - (1/2 √3)²
= 2 + (1/2 √3) - (3/4)
= 5/4 + 1/2 √3
= 1/2(5/2 + √3)

c. (cos 45°)/(Sec 30° + Csc 30°)
= (1/2 √2)/(2/3 √3 + 2)
= (3/2 √2)/(2√3 + 6)

Rasionalkan...
= (3√6 - 9√2)/(12 - 6)
= (3√6 - 9√2)/6
= (√6 - 3√2)/2
= 1/2(√6 - 3√2)

d. (Sin 30° + Tan 45° - csc 60°)/(sec 30° + cos 60° + cot 45°)
= (1/2 + 1 - 2/3 √3)/(2/3 √3 + 1/2 + 1)
= (3 + 6 - 4√3)/(4√3 + 3 + 6)
= (9 - 4√3)/(4√3 + 9)

Rasionalkan...
= (72√3 - 129)/(48 - 81)
= (72√3 - 129)/(-33)
= (129 - 72√3)/33
= 1/33 (129 - 72√3)

2.
a + b = 10 » a = 10 - b
<A = 30°
<B = 45°

a/sin A = b/sin B
(10 - b)/sin 30 = b/sin 45
(10 - b) sin 45 = b sin 30
(10 - b) 1/2 akar2 = b * 1/2
10 akar2 - b akar2 = b
b + b akar2 = 10 akar2
b( 1+ akar2) = 10 akar2
b = 10 akar2/(1 + akar2)
b = (20 - 10 akar2) cm