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📐 त्रिकोणमिति : महत्वपूर्ण सूत्र 📐

🔴 योग सूत्र
➭ Sin(A+B) = SinACosB+CosASinB
➭ Sin(A-B) = SinACosB-CosASinB
➭ Cos(A+B) = CosACosB-SinASinB
➭ Cos(A-B) = CosACosB+SinASinB

🔴 अन्तर सूत्र
➭ tan(A+B) = tanA+tanB/1-tanAtanB
➭ tan(A-B) = tanA-tanB/1+tanAtanB

🔴 C-D सूत्र
➭ SinC+SinD = 2Sin(C+D/2) Cos(C-D/2)
➭ SinC-SinD = 2Cos(C+D/2) Sin(C-D/2)
➭ CosC+CosD = 2Cos(C+D/2) Cos(C-D/2)
➭ CosC-CosD = 2Sin(C+D/2) Sin(D-C/2)
➭ CosC-CosD = -2Sin(C+D/2) Sin(C-D/2)

🔴 रूपांतरण सूत्र
➛ 2SinACosB = Sin(A+B)+Sin(A-B)
➛ 2CosASinB = Sin(A+B)-Sin(A-B)
➛ 2CosACosB = Cos(A+B)+Cos(A-B)
➛ 2SinASinB = Cos(A-B)-Cos(A+B)

🔴 द्विक कोण सूत्र
➛ Sin2A = 2SinACosA
➛ Cos2A = Cos²A-Sin²A = 2Cos²-1 = 1-2Sin²A
➛ tan2A = 2tanA/1-tan²A
➛ Sin2A = 2tanA/1+tan²A
➛ Cos2A = 1-tan²A/1+tan²A

🔴विशिष्ट सूत्र
➛ Sin(A+B)Sin(A-B) = Sin²A-Sin²B
= Cos²B-Cos²A
➛ Cos(A+B)Cos(A-B) = Cos²A-Sin²B = Cos²B-Sin²A

🔴 त्रिक कोण सूत्र
➛ Sin3A = 3SinA-4Sin³A
➛ Cos3A = 4Cos³A-3CosA
➛ tan3A = 3tanA-tan³A/1-3tan²A

🔴 महत्वपूर्ण सर्वसमिकाएं
➛ Sin²θ+Cos²θ = 1
➭ Sin²θ = 1-Cos²θ
➭ Cos²θ = 1-Sin²θ
➛ 1+tan²θ = Sec²θ
➭ Sec²θ-tan²θ = 1
➭ tan²θ = Sec²θ-1
➛ 1+Cot²θ = Cosec²θ
➭ Cosec²θ-Cot²θ = 1
➭ Cot²θ = Cosec²θ-1

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╭───────────────────╮
⚡️ Daily Current Affairs : 29-09-2021 ⚡️
╰───────────────────╯

1. For how long has the Delhi Pollution Control Committee banned the sale of firecrackers and fireworks in the National Capital Region?
Ans : By January 01, 2022

2. Which state Congress party president Navjot Singh Sidhu has resigned from his post?
Ans : Punjab

3. The footballer of England's world winning team has passed away at the age of 83, what was his name?
Ans : Roger Hunt

4. Which board has been announced by the Central Government and the Ministry of Defense to be dissolved from October 01?
Ans : Ordnance Factory Board (OFB)

5. National Commission for Women has launched a program for training for women in which field?
Ans : Dairy Farming

6. C.K. Ranganathan has been appointed as the President of which association?
Ans : All India Management Association

7. Today (September 29) is being celebrated as which day all over the world?
Ans : World Heart Day

8. How many new cases of corona have been reported in the country in the last 24 hours?
Ans : 18,870 Cases (378 Deaths)

9. For how long has the Haryana state government extended the ban on gutkha, pan masala in the state?
Ans : September 2022

10. Which tennis doubles title has been won by Sania Mirza and her Chinese partner Zhang Shuai?
Ans : Ostrava Open Women's Doubles Title

4×4+1×1=17
5×5+2×2=29
6×6+3×3=45
9×9+8×8=145
145✅

#ONE_WORD_SUBSTITUTION

1. Polyandry – the practice of marrying more than one husband at a time
2. Philogynist – a lover of womankind
3. Plebiscite – (a decision made by) votes of all qualified citizens
4. Philanderer – one, who amuses himself by love making
5. Philistine – one who does not care for art and literature
6. Plutocracy – government by the rich
7. Pseudonym – an imaginary name assumed by an author for disguise
8. Posthumous – a child born after the death of his father or the book published after the death of the writer
9. Panacea – a remedy for all diseases
10. Pediatrician – a person, who is specialist in child diseases
11. Platitude – ordinary remarks often repeated
12. Pedant – one, who makes a vain display of his knowledge
13. Polyglot – one, who speaks many languages
14. Paleography – the study of ancient writing
15. Posse – a number of policemen called to quell a riot
16. Parole – pledge given by a prisoner for temporary release, not to escape
17. Pedestrian – one, who goes on foot
18. Portable – that can be carried easily
19. Quarantine – an act of separation from other persons to avoid infection
20. Rhetoric – the art of elegant speech or writing
21. Regicide – murder of King or Queen
22. Sacrilege – violating or profaning religious things/places
23. Sculptor – one, who cuts in stones
24. Suicide – murder of oneself
25. Stable – a place for horses
26. Somnambulist – a person, who walks in sleep
27. Somniloquist – a person, who talks in sleep
28. Souvenir – a thing kept as a reminder of a person, place or event
29. Swan song – the last work (literary) of a writer
30. Sot, Toper – one, who is a habitual drunkard
31. Sinecure – a job with high salary but little responsibility
32. Stoic – a person, who is indifferent to pleasure and pain and has control over his passions
33. Sanatorium – a place for the sick to recover health
34. Sororicide – murder of sister
35. Triennial – an event which happens once in three years
36. Truant – a person/student who absents himself from class or duty without permission
37. Teetotaller – one, who does not take any intoxicating drink
38. Transparent – that which can be seen through
39. Theocracy – government by religious principles
40. Uxorious – one extremely fond of one’s wife
41. Utopia – an imaginary perfect social and political system
42. Uxoricide – murder of wife
43. Verbatim – repetition of speech or writing word for word
44. Volunteer – one, who offers one’s services
45. Virgin – a woman who has no sexual experience
46. Versatile – interested in and clever at many different things
47. Veteran – one, who has a long experience of any occupation
48. Venial – a fault that may be forgiven
49. Velodrome -- A track designed for cycling
50. Genophobia -- Fear of sex