Algebra and Abbreviations

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(α+в+¢)²= α²+в²+¢²+2(αв+в¢+¢α)
1. (α+в)²= α²+2αв+в²
2. (α+в)²= (α-в)²+4αв b
3. (α-в)²= α²-2αв+в²
4. (α-в)²= f(α+в)²-4αв
5. α² + в²= (α+в)² - 2αв.
6. α² + в²= (α-в)² + 2αв.
7. α²-в² =(α + в)(α - в)
8. 2(α² + в²) = (α+ в)² + (α - в)²
9. 4αв = (α + в)² -(α-в)²
10. αв ={(α+в)/2}²-{(α-в)/2}²
11.(α + в + ¢)²=α²+в² + ¢² +2(αв + в¢ + ¢α)
12. (α + в)³ = α³ + 3α²в + 3αв² + в³
13. (α + в)³ = α³ + в³ + 3αв(α + в)
14. (α-в)³=α³-3α²в+3αв²-в³
15. α³ + в³ = (α + в) (α² -αв + в²)
16. α³ + в³ = (α+ в)³ -3αв(α+ в)
17. α³ -в³ = (α -в) (α² + αв + в²)
18. α³ -в³ = (α-в)³ + 3αв(α-в)

ѕιη0° =0
ѕιη30° = 1/2
ѕιη45° = 1/√2
ѕιη60° = √3/2
ѕιη90° = 1
¢σѕ ιѕ σρρσѕιтє σƒ ѕιη
тαη0° = 0
тαη30° = 1/√3
тαη45° = 1
тαη60° = √3
тαη90° = ∞
¢σт ιѕ σρρσѕιтє σƒ тαη
ѕє¢0° = 1
ѕє¢30° = 2/√3
ѕє¢45° = √2
ѕє¢60° = 2
ѕє¢90° = ∞

¢σѕє¢ ιѕ σρρσѕιтє σƒ ѕє¢
2ѕιηα¢σѕв=ѕιη(α+в)+ѕιη(α-в)
2¢σѕαѕιηв=ѕιη(α+в)-ѕιη(α-в)
2¢σѕα¢σѕв=¢σѕ(α+в)+¢σѕ(α-в)
2ѕιηαѕιηв=¢σѕ(α-в)-¢σѕ(α+в)
ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
» ¢σѕ(α+в)=¢σѕα ¢σѕв - ѕιηα ѕιηв.
» ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
» ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
» тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
» тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
» ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
» ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
» ѕιη(α+в)=ѕιηα ¢σѕв+ ¢σѕα ѕιηв.
» ¢σѕ(α+в)=¢σѕα ¢σѕв +ѕιηα ѕιηв.
» ѕιη(α-в)=ѕιηα¢σѕв-¢σѕαѕιηв.
» ¢σѕ(α-в)=¢σѕα¢σѕв+ѕιηαѕιηв.
» тαη(α+в)= (тαηα + тαηв)/ (1−тαηαтαηв)
» тαη(α−в)= (тαηα − тαηв) / (1+ тαηαтαηв)
» ¢σт(α+в)= (¢σтα¢σтв −1) / (¢σтα + ¢σтв)
» ¢σт(α−в)= (¢σтα¢σтв + 1) / (¢σтв− ¢σтα)
α/ѕιηα = в/ѕιηв = ¢/ѕιη¢ = 2я
» α = в ¢σѕ¢ + ¢ ¢σѕв
» в = α ¢σѕ¢ + ¢ ¢σѕα
» ¢ = α ¢σѕв + в ¢σѕα
» ¢σѕα = (в² + ¢²− α²) / 2в¢
» ¢σѕв = (¢² + α²− в²) / 2¢α
» ¢σѕ¢ = (α² + в²− ¢²) / 2¢α
» Δ = αв¢/4я
» ѕιηΘ = 0 тнєη,Θ = ηΠ
» ѕιηΘ = 1 тнєη,Θ = (4η + 1)Π/2
» ѕιηΘ =−1 тнєη,Θ = (4η− 1)Π/2
» ѕιηΘ = ѕιηα тнєη,Θ = ηΠ (−1)^ηα

1. ѕιη2α = 2ѕιηα¢σѕα
2. ¢σѕ2α = ¢σѕ²α − ѕιη²α
3. ¢σѕ2α = 2¢σѕ²α − 1
4. ¢σѕ2α = 1 − ѕιη²α
5. 2ѕιη²α = 1 − ¢σѕ2α
6. 1 + ѕιη2α = (ѕιηα + ¢σѕα)²
7. 1 − ѕιη2α = (ѕιηα − ¢σѕα)²
8. тαη2α = 2тαηα / (1 − тαη²α)
9. ѕιη2α = 2тαηα / (1 + тαη²α)
10. ¢σѕ2α = (1 − тαη²α) / (1 + тαη²α)
11. 4ѕιη³α = 3ѕιηα − ѕιη3α
12. 4¢σѕ³α = 3¢σѕα + ¢σѕ3α
〰〰〰〰〰〰〰〰〰〰〰
» ѕιη²Θ+¢σѕ²Θ=1
» ѕє¢²Θ-тαη²Θ=1
» ¢σѕє¢²Θ-¢σт²Θ=1
» ѕιηΘ=1/¢σѕє¢Θ
» ¢σѕє¢Θ=1/ѕιηΘ
» ¢σѕΘ=1/ѕє¢Θ
» ѕє¢Θ=1/¢σѕΘ
» тαηΘ=1/¢σтΘ
» ¢σтΘ=1/тαηΘ
» тαηΘ=ѕιηΘ/¢σѕΘ

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விரிவான தகவல்!
B. A. — Bachelor of Arts
M. A. — Master of Arts
B. Sc. — Bachelor of Science
M. Sc. — Master of Science
B. Sc. Ag. — Bachelor of Science in
Agriculture
M. Sc. Ag. — Master of Science in Agriculture
M. B. B. S. — Bachelor of Medicine and Bachelor of Surgery
M. D. — Doctor of Medicine
M. S. — Master of Surgery
Ph. D. / D. Phil. — Doctor of Philosophy (Arts & Science)
D. Litt./Lit. — Doctor of Literature / Doctor of Letters
D. Sc. — Doctor of Science
B. Com. — Bachelor of Commerce
M. Com. — Master of Commerce
Dr. — Doctor
B. P. — Blood Pressure
Mr. — Mister
Mrs. — Mistress
M.S. — miss (used for female married & unmarried)
Miss — used before unmarried girls)
M. P. — Member of Parliament
M. L. A. — Member of Legislative Assembly
M. L. C. — Member of Legislative Council
P. M. — Prime Minister
C. M. — Chief Minister
C-in-C — Commander-In-Chief
L. D. C. — Lower Division Clerk
U. D. C. — Upper Division Clerk
Lt. Gov. — Lieutenant Governor
D. M. — District Magistrate
V. I. P. — Very Important Person
I. T. O. — Income Tax Officer
C. I. D. — Criminal Investigation Department
C/o — Care of
S/o — Son of
C. B. I. — Central Bureau of Investigation
G. P. O. — General Post Office
H. Q. — Head Quarters
E. O. E. — Errors and Omissions Excepted
Kg. — Kilogram
Kw. — Kilowatts

👉Gm. — Gram
👉Km. — Kilometer
👉Ltd. — Limited
👉M. P. H. — Miles Per Hour
👉KM. P. H. — Kilometre Per Hour
👉P. T. O. — Please Turn Over
👉P. W. D. — Public Works Department
👉C. P. W. D. — Central Public Works Department
👉U. S. A. — United States of America
👉U. K. — United Kingdom (England)
👉U. P. — Uttar Pradesh
👉M. P. — Madhya Pradesh
👉H. P. — Himachal Pradesh
👉U. N. O. — United Nations Organization
👉W. H. O. — World Health Organization
👉B. B. C. — British Broadcasting Corporation
👉B. C. — Before Christ
👉A. C. — Air Conditioned
👉I. G. — Inspector General (of Police)
👉D. I. G. — Deputy Inspector General (of Police)
👉S. S. P. — Senior Superintendent of Police
👉D. S. P. — Deputy Superintendent of Police
👉S. D. M. — Sub-Divisional Magistrate
👉S. M. — Station Master
👉A. S. M. — Assistant Station Master
👉V. C. — Vice-Chancellor
👉A. G. — Accountant General
👉C. R. — Confidential Report
👉I. A. S. — Indian Administrative Service
👉I. P. S. — Indian Police Service
👉I. F. S. — Indian Foreign Service or Indian

Forest Service
🔹I.R.S. — Indian Revenue Service
🔹P.C.S. — Provincial Civil Service
🔹M.E.S. — Military Engineering Service

Full Form Of Some technical Words
VIRUS - Vital Information Resource
UnderSeized.
3G -3rd Generation.
GSM - Global System for Mobile
Communication.
CDMA - Code Divison Multiple
Access.
UMTS - Universal MobileTelecommunication
System.
SIM - Subscriber Identity Module .
AVI = Audio Video Interleave
RTS = Real Time Streaming
SIS = Symbian
OS Installer File
AMR = Adaptive Multi-Rate Codec
JAD = Java Application Descriptor
JAR = Java Archive
JAD = Java Application Descriptor
3GPP = 3rd Generation Partnership Project
3GP = 3rd Generation Project
MAA=Mehboob Anwar Ansari
MP3 = MPEG player lll
MP4 = MPEG-4 video file
AAC = Advanced Audio Coding
GIF= Graphic InterchangeableFormat
JPEG = Joint Photographic Expert Group
JPEG = Joint Photographic Expert Group
BMP = Bitmap
SWF = Shock Wave Flash
WMV = Windows Media Video
WMA = Windows Media Audio
WAV = Waveform Audio
PNG = Portable Network Graphics
DOC =Document (MicrosoftCorporation)
PDF = Portable Document Format
M3G = Mobile 3D Graphics
M4A = MPEG-4 Audio File
NTH = Nokia Theme (series 40)
THM = Themes (Sony Ericsson)
MMF =
Synthetic Music Mobile Application File
NRT = Nokia Ringtone
XMF = Extensible Music File
WBMP = Wireless Bitmap Image
DVX = DivX Video
HTML = Hyper Text Markup Language
WML =
Wireless Markup Language.

🔹CD -Compact Disk.
🔹DVD - Digital Versatile Disk.
🔹CRT - Cathode Ray Tube.
🔹DAT - Digital Audio Tape.
🔹DOS - Disk Operating System.
🔹GUI -Graphical User Interface.
🔹HTTP - Hyper Text Transfer Protocol.
🔹IP - Internet Protocol.
🔹ISP - Internet Service Provider.
🔹TCP - Transmission Control Protocol.
🔹UPS - UninterruptiblePower Supply.
🔹HSDPA -High Speed Downlink Packet Access.
🔹EDGE - Enhanced Data Rate for
🔹GSM- [GlobalSystem for Mobile
Communication]
Evolution.
🔹VHF - Very High Frequency.
🔹UHF - Ultra High Frequency.
🔹GPRS - General
PacketRadio Service.
🔹WAP - Wireless ApplicationProtocol.
🔹TCP - Transmission ControlProtocol.
🔹ARPANET - Advanced Research Project
Agency Network.
🔹IBM - International Business Machines.
🔹HP - Hewlett Packard.
🔹AM/FM - Amplitude/ Frequency Modulation.

Here are Toll Free numbers in
India...

Airlines
Indian Airlines - 1800 180 1407
Jet Airways - 1800 225 522
Spice Jet - 1800 180 3333
Air India - 1800 227 722
Kingfisher -1800 180 0101

Banks
ABN AMRO - 1800 112 224
Canara Bank - 1800 446 000
Citibank - 1800 442 265
Corporation Bank - 1800 443 555
Development Credit Bank - 1800
225 769
HDFC Bank - 1800 227 227
ICICI Bank - 1800 333 499
ICICI Bank NRI -1800 224 848
IDBI Bank -1800 116 999
Indian Bank -1800 425 1400
ING Vysya -1800 449 900
Kotak Mahindra Bank - 1800 226
022
Lord Krishna Bank -1800 112 300
Punjab National Bank - 1800 122
222
State Bank of India - 1800 441 955
Syndicate Bank - 1800 446 655

Automobiles
Mahindra Scorpio -1800 226 006
Maruti -1800 111 515
Tata Motors - 1800 255 52
Windshield Experts - 1800 113 636

Computers / IT
Adrenalin - 1800 444 445
AMD -1800 425 6664
Apple Computers-1800 444 683
Canon -1800 333 366
Cisco Systems- 1800 221 777