त्रिकोणमिति : महत्वपूर्ण सूत्र (IMP 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 27 views15:24