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Purvi Mishra 😊🙏✌️

📚 The Hindu Vocabulary - Friday, 19 February 2021 📚


🖍 COMPASSION (NOUN): (दया): pity
Synonyms: sympathy, feeling
Antonyms: indifference
Example Sentence:
The victims of any calamity should be treated with compassion.

🖍 FEASIBLE (ADJECTIVE): (संभावित): probable
Synonyms: likely, conceivable
Antonyms: impossible
Example Sentence:
He gave the most feasible explanation.

🖍 REBUT (VERB): (खंडन करना): refute
Synonyms: deny, disprove
Antonyms: confirm
Example Sentence:
He attempts to rebut the assertion made by the prosecution witness.

🖍 EXTRANEOUS (ADJECTIVE): (बाहरी): external
Synonyms: outside, exterior
Antonyms: intrinsic
Example Sentence:
When the transmitter pack is turned off no extraneous noise is heard.

🖍 DELIBERATE (ADJECTIVE): (जानबूझकर): intentional
Synonyms: calculated, conscious
Antonyms: accidental
Example Sentence:
He made a deliberate attempt to provoke conflict.

🖍 UBIQUITOUS (ADJECTIVE): (सर्व-भूत): omnipresent
Synonyms: ever-present, everywhere
Antonyms: extraordinary
Example Sentence:
His ubiquitous influence was felt by all the family.

🖍 ALLEGIANCE (NOUN): (निष्ठा): loyalty
Synonyms: faithfulness, fidelity
Antonyms: disloyalty
Example Sentence:
Those wishing to receive citizenship must swear allegiance to the republic.

🖍 VILIFY (VERB): (कलंक लगाना): disparage
Synonyms: denigrate, defame
Antonyms: commend
Example Sentence:
He has been vilified in the press.

🖍 IMBECILE (ADJECTIVE): (मूर्खतापूर्ण): stupid
Synonyms: foolish, idiotic
Antonyms: intelligent
Example Sentence:
Try not to make imbecile remarks.

🖍 OUTRAGEOUS (ADJECTIVE): (अपमानजनक): shocking
Synonyms: disgraceful, scandalous
Antonyms: acceptable
Example Sentence:
It was an outrageous act of bribery.

📐 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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