Identitates Trigonometricas

Identitates Trigonometricas

• COSA - COSB = -2sin(A+B)sin(A-B): Relacio entre cosenos de A e B.
• sin 2A = 2sinA.COSA: Relacion que exprime sin de un angulo double in terminos de sin e cos del angulo A, complemente con tanA.
• COS2A = COSA - Sin²A: Formula per calcular coseno de un angulo double.
• tan 2A = (2tanA)/(1-tan²A) = (1 + tan²A)/(1 - tan²A) = (2 COS²A-1)/(sin²A): Diverse maneras de exprimer tangente de un angulo double.
• sin 3A = 3 sinA - 4sin³A: Formula per calcular sin de un angulo triple.
• COS 3A = 4COS³A-3COSA: Predicate per calcular coseno de un angulo triple.
• tan 3A = (3tana-tan³A)/(1-3tan²A): Formule pro calcular tangente de un angulo triple.
• COS(A-B) - COS(A+B) = 2sinA.SinB: Relation util pro calcular diferencias e summas de cosenos.
• COSA = cos²(A/2) - sin²(A/2): Relacion intermedie per determinar coseno de un angulo usante angulos half.
• tan A ± tanB = sin(A±B)/(COSA.COSB): Dependencia entre tangentes, seno, e coseno.
• cot A ± cotB = COS(A±B)/(SinA.sinB): Formula correlata per cotangente.
• 1 ± tan A.tanB = cos(A±B)/(COSA.COSB): Relacion util inter tan e cos.
• (1 - tan²A)/(1 + tan²A) = COS2A: Formula utilisante tangente per obtener coseno double.
• (2tana)/(1 + tan²A) = Sin2A: Relacion inter tangente e sin double.
• 1 + sin²A = (COSA + SinA)²: Identitate fundamentale relationante sin e coseno.
• sin(60° - 0) sin(60° + 0) = 1.sin 30: Identitate pro calcular sinum con angulos specific.
• Cos(60° - 0) cos(60° + 0) = 1 + cos30: Relation trigonometric pertinente a coseno in angulos specific.
• a sinθ + b cosθ = √(a²+b²) (sin(θ + φ)): Formula vectorial que combina sin e cos in un format geometric.

Identitates Trigonometric

• Differentiation of Cosines: $\cos{A} - \cos{B} = -2\sin{\left(\frac{A+B}{2}\right)} \cdot \sin{\left(\frac{A-B}{2}\right)}$
• Double Angle Formula for Sine: $\sin{2A} = 2 \sin{A} \cos{A}$
• Double Angle Formula for Cosine: $\cos{2A} = \cos^2{A} - \sin^2{A}$
• Double Angle Formula for Tangent: $\tan{2A} = \frac{2 \tan{A}}{1 - \tan^2{A}}$
• Triple Angle Formula for Sine: $\sin{3A} = 3 \sin{A} - 4 \sin^3{A}$
• Triple Angle Formula for Cosine: $\cos{3A} = 4 \cos^3{A} - 3 \cos{A}$
• Triple Angle Formula for Tangent: $\tan{3A} = \frac{3 \tan{A} - \tan^3{A}}{1 - 3 \tan^2{A}}$
• Difference of Cosines: $\cos{(A+B)} - \cos{(A-B)} = -2 \sin{A} \sin{B}$
• Cosine Half Angle Identity: $\cos{A} = \cos^2{\left(\frac{A}{2}\right)} - \sin^2{\left(\frac{A}{2}\right)}$
• Sum and Difference of Tangents: $\tan{A} \pm \tan{B} = \frac{\sin{(A \pm B)}}{\cos{A} \cos{B}}$
• Sum of Cotangents: $\cot{A} + \cot{B} = \frac{\cos{(A+B)}}{\sin{A} \sin{B}}$
• Sum of Tangents with Cosine: $1 \pm \tan{A} \cdot \tan{B} = \frac{\cos{(A \pm B)}}{\cos{A} \cos{B}}$
• Cosine of Double Angle in Terms of Tangent: $\frac{1-\tan^2{A}}{1 + \tan^2{A}} = \cos{2A}$
• Simplified Tangent Identity: $2 \tan{A} = \frac{1 + \tan^2{A}}{1 + \tan^2{A}}$
• Quadratic Sine Representation: $1 \pm \sin{2A} = (\cos{A} \pm \sin{A})^2$
• Product of Sine Functions: $\sin{\theta} \sin{(60^\circ - \theta)} \sin{(60^\circ + \theta)} = \frac{1}{4} \sin{3 \theta}$
• Product of Cosine Functions: $\cos{\theta} \cos{(60^\circ - \theta)} \cos{(60^\circ + \theta)} = \frac{1}{4} \cos{3 \theta}$
• Linear Combination of Sine and Cosine: $a \sin{\theta} + b \cos{\theta} = \sqrt{a^2 + b^2} \left( \sin{(\theta + \phi)}\right)$