Bài tập tính đạo hàm

tieỏt 10: Luyeọn taọp
PHệễNG TRèNH LệễẽNG GIAC Cễ BAN

TỐM TẮT
Giả sử u, v là những biểu thức theo x. Ta có:
+ sin u = sin v ⇔ u = v + k2π
u = π - v + k2π (k ∈ Z)
+ cos u = cos v ⇔ u = v + k2π
u = - v + k2π (k ∈ Z)
+ tan u = tan v ⇔ u, v ≠ π/2 + mπ
u = v + kπ (m, k ∈ Z)
+ cot u = cot v ⇔ u, v ≠ mπ
u = v + kπ (m, k ∈ Z)

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Gụùi yự traỷ lụứi
a) sin (x - 3) = 1/4 x 3 = arcsin1/4 + k2
x - 3 = - arcsin1/4 + k2
x = 3 + arcsin1/4 + k2
x = 3 + - arcsin1/4 + k2 (k Z)
b) sin 5x = 1 5x = /2 + k 2 (k Z)

x = /10 + k 2/5 (k Z)

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BT2: Giaûi caùc phöông trình sau

a) cos (x+2) = 2/5
b) cos 4x = cos 20
0

c) cos (2x/3 - π/3) = -1/2
d) tan (2x – 15
0
) = 1;
-180
0
≤ x ≤ 120
0



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(

•
b) cos 4x = cos 20
0

•
⇔ 4x = 20
0
+ k360
0
•
4x = -20
0
+ k360
0
(k ∈ Z)
•
⇔ x = 5
0
+ k 90
0
•
x = -5
0

+ k 90
0
(k ∈ Z)

c) cos (2x/3 - π/3) = -1/2
⇔ cos (2x/3 - π/3) = cos (2π/3)
⇔ 2x/3 - π/3= 2π/3 + k 2π
2x/3 - π/3= - 2π/3 + k 2π (k ∈ Z)
⇔ 2x/3 = π + k 2π
2x/3 = - π/3+ k 2π (k ∈ Z)
⇔ x = 3π/2 + k 3π
x = - π/2 + k 3π (k ∈ Z)

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