त्रिकोणमिति : महत्वपूर्ण सूत्र।।

Trigonometry Important Formula

🍎 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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