UPSC CSE Prelims 2024

त्रिकोणमिति : महत्वपूर्ण सूत्र


  📊 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


🖌

1. Work = force × distance

कार्य = बल × दूरी


2. Energy = force × distance

ऊर्जा = बल × दूरी


3. Speed = distance / time

गति = दूरी / समय


4. Velocity= displacement / time

वेग = विस्थापन / समय


5. Electric field = electrical force/charge

विद्युत क्षेत्र= वैद्युत बल/आवेश


6. Force = force/area

प्रतिबल=बल/क्षेत्रफल


7. Volume = length × width × height

आयतन = लंबाई × चौड़ाई × ऊंचाई


8. Mass density = mass/volume

द्रव्यमान घनत्व =द्रव्यमान/आयतन


9. Acceleration =velocity / time

त्वरण = वेग / समय


10. Power = work / time

शक्ति = कार्य / समय


11. Pressure = force / area

दाब =बल/क्षेत्रफल


11. Momentum = mass × velocity

संवेग = द्रव्यमान × वेग


13. Area (A) = Length × Width

क्षेत्रफल ( A ) = लम्बाई × चौड़ाई


14. Force (F) = Mass × Acceleration

बल ( F ) = द्रव्यमान × त्वरण


15. Pressure Energy = Pressure × Volume

दाब ऊर्जा = दाब × आयतन


16. Impulse = force × time

आवेग = बल × समय


17. Linear momentum = mass × velocity

रैखिक संवेग = द्रव्यमान × वेग


18. Kinetic energy = 1/2 mv²

गतिज ऊर्जा = 1/2 mv²


19. Mechanical energy = kinetic energy + potential energy

यांत्रिक ऊर्जा = गतिज ऊर्जा + स्थितिज ऊर्जा


20. Angular momentum = Inertial × Angular velocity

कोणीय संवेग = जड़त्वाघूर्ण × कोणीय वेग



Post a Comment

Cookie Consent
We serve cookies on this site to analyze traffic, remember your preferences, and optimize your experience.
Oops!
It seems there is something wrong with your internet connection. Please connect to the internet and start browsing again.
AdBlock Detected!
We have detected that you are using adblocking plugin in your browser.
The revenue we earn by the advertisements is used to manage this website, we request you to whitelist our website in your adblocking plugin.
Site is Blocked
Sorry! This site is not available in your country.
//disable Text Selection and Copying