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Popular >

verificar 3cos^2(a)-2=1-3sin^2(a)

Solución

verificar

3 cos^{2} (a) - 2 = 1 - 3 sin^{2} (a)

Verdadero

Pasos de solución

3 cos^{2} (a) - 2 = 1 - 3 sin^{2} (a)

Manipular el lado derecho

3 cos^{2} (a) - 2

Re-escribir usando identidades trigonométricas

3 cos^{2} (a) - 2

Utilizar la identidad pitagórica:

cos^{2} (x) + sin^{2} (x) = 1

cos^{2} (x) = 1 - sin^{2} (x)

= 3 (1 - sin^{2} (a)) - 2

Simplificar

3 (1 - sin^{2} (a)) - 2 : - 3 sin^{2} (a) + 1

3 (1 - sin^{2} (a)) - 2

Expandir

3 (1 - sin^{2} (a)) : 3 - 3 sin^{2} (a)

3 (1 - sin^{2} (a))

Poner los parentesis utilizando:

a (b - c) = ab - a c

a = 3, b = 1, c = sin^{2} (a)

= 3 \cdot 1 - 3 sin^{2} (a)

Multiplicar los numeros:

3 \cdot 1 = 3

= 3 - 3 sin^{2} (a)

= 3 - 3 sin^{2} (a) - 2

Simplificar

3 - 3 sin^{2} (a) - 2 : - 3 sin^{2} (a) + 1

3 - 3 sin^{2} (a) - 2

Agrupar términos semejantes

= - 3 sin^{2} (a) + 3 - 2

Sumar/restar lo siguiente:

3 - 2 = 1

= - 3 sin^{2} (a) + 1

= - 3 sin^{2} (a) + 1

= - 3 sin^{2} (a) + 1

= - 3 sin^{2} (a) + 1

= 1 - 3 sin^{2} (a)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

tan (A) = tan (A) csc^{2} (A) + cot (- A)

\frac{1}{1 + sin ( x )} = (sec (x) - tan (x)) sec (x)

(sec (x) + tan (x))^{2} = 1

tan (A) cot (A) = cos^{2} (A) + sin^{2} (A)

tan (a) + cot (a) = \frac{2}{sin ( 2 a )}