Bài giảng Biến đổi lượng giác - Phần V: Biến đổi lượng giác

TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC 
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 sintan
cos
 

.  coscot
sin
 

. 
 2 2sin cos 1    .  tan .cot 1   . 
 2
2
1
1 tan
cos
  

.  2
2
1
1 cot
sin
  

. 
BA ̀I TẬP A ́P DỤNG 
Bài	1. Chứng minh ca ́c đẳng thư ́c sau 
1/ 2 2 2cos x sin x 1 2 sin x   . 2/ 2 22cos x 1 1 2 sin x   . 
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3/ 2 23 4 sin x 4 cos x 1   . 4/ sin x cot x cos x tan x sin x cos x   . 
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5/ 4 4 2 2sin x cos x 1 2 sin x cos x   . 6/ 4 4 2 2cos x sin x cos x sin x   . 
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7/   24 cos x 3 1 2 sin x 1 2 sin x    . 8/   2 2 21 cosx sin x cosx cos x sin x    . 
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PHẦN V: BIẾN ĐỔI LƯỢNG GIÁC 
A – HỆ THỨC LƯỢNG GIÁC CƠ BẢN 
TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC 
2 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 
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9/ 4 4 2 2sin x cos x 1 2cos x 2sin x 1     . 10/ 3 3sin x cos x sin x cos x sin x cos x  . 
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11/ 2 2 2 2tan x sin x tan x sin x  . 12/ 2 2 2 2cot x cos x cot x cos x  . 
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Bài	2. Chứng minh các đẳng thư ́c sau 
1/ 1tan x cotx
sin x cos x
  . 2/ 1 cos x sin x
sin x 1 cos x
   . 
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3/ 1 1 1
1 tan x 1 cotx
   . 4/ 
21 11 1 tan x 0
cos x cos x
               
. 
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5/ 
2
2
2
1 sin x
1 2 tan x
1 sin x
  

. 6/ tan x tan ytan x tan y
cotx cot y
  . 
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TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC 
ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 3 | THBTN 
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7/ 4
2 4
2 1
1 cot x
sin x sin x
   . 8/ cos x 1tan x
1 sin x cos x
  . 
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9/   2 11 cos x 1 cot x
1 cos x
    . 10/ 
1 cos x 1 cos x 4 cot x
1 cos x 1 cos x sin x
    . 
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11/ sin x 1 cos x 2
1 cos x sin x sin x
  . 12/ 
sin x cos x 1 cos x
sin x cos x 1 1 sin x
     . 
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13/ 
2
2
sin x 2cos x 1 cos x
1 cos x2 cos x cos x
  
 
. 14/ sin x cos x 1 2cos x
1 cos x sin x cos x 1
     . 
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Bài	3. Chứng minh các đẳng thư ́c sau 
TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC 
4 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.341 
1/ 6 6 2 2sin x cos x 1 3 sin x cos x   . 
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2/   6 6 2 2 2 2sin x cos x sin x cos x 1 sin x cos x    . 
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3/  28 8 2 2 4 4sin x cos x 1 2 sin x cos x 2 sin x cos x    . 
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4/   8 8 2 2 2 2sin x cos x sin x cos x 1 2sin x cos x    . 
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Bài	4. Chứng minh các đẳng thư ́c sau 
1/   1 sin x cos x tan x 1 cos x 1 tan x      . 
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2/   1 tan x 1 cot x sin x cos x 1 2 sin x cos x    . 
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TÀI LIỆU HỌC TẬP TOÁN 10 – CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢNG GIÁC 
ADMIN TRẦN VĂN TÀI – 0977.413.341 - TOÁN HỌC BẮC–TRUNG–NAM 5 | THBTN 
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3/      22 21 tan x cos x 1 cotx sin x sin x cos x     . 
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4/ 2 2sin x tan x cos x cot x 2 sin x cos x tan x cot x    . 
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5/ 2 2 2 2 2sin x tan x 4 sin x tan x 3 cos x 3    . 
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Bài	5. Chứng minh các đẳng thư ́c sau 
1/ 
2 2sin cos tan 1
1 2 sin cos tan 1
         . 2/ 
2 2
6
2 2
tan sin
tan
cot cos
    
  
. 
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3/ 
2 2cos sin
1 sin cos
1 tan 1 cot
     
   
. 4/  3
tan sin 1
sin cos 1 cos
   
   
. 
TÀI LIỆU HỌC TẬP TOÁN 10- CHẤT LƯỢNG BÀI GIẢNG: BIẾN ĐỔI LƯỢN GIÁC 
6 | THBTN – CA FILE WORD LIÊN HỆ - THẦY TÀI: 0977.413.34