cos^2(A)+sin^2(A)= 1/(sin^2(A))

Solución

cos^{2} (A) + sin^{2} (A) = \frac{1}{sin ^{2} ( A )}

A = \frac{π}{2} + 2 πn, A = \frac{3 π}{2} + 2 πn

Pasos de solución

cos^{2} (A) + sin^{2} (A) = \frac{1}{sin ^{2} ( A )}

Restar

\frac{1}{sin ^{2} ( A )}

de ambos lados

cos^{2} (A) + sin^{2} (A) - \frac{1}{sin ^{2} ( A )} = 0

Simplificar

cos^{2} (A) + sin^{2} (A) - \frac{1}{sin ^{2} ( A )} : \frac{cos ^{2} ( A ) sin ^{2} ( A ) + sin ^{4} ( A ) - 1}{sin ^{2} ( A )}

\frac{cos ^{2} ( A ) sin ^{2} ( A ) + sin ^{4} ( A ) - 1}{sin ^{2} ( A )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cos^{2} (A) sin^{2} (A) + sin^{4} (A) - 1 = 0

Re-escribir usando identidades trigonométricas

- 1 + sin^{2} (A) = 0

Usando el método de sustitución

sin (A) = 1, sin (A) = - 1

sin (A) = 1 : A = \frac{π}{2} + 2 πn

sin (A) = - 1 : A = \frac{3 π}{2} + 2 πn

Combinar toda las soluciones

A = \frac{π}{2} + 2 πn, A = \frac{3 π}{2} + 2 πn

cos (4 θ) = 1

tan (2 x) + sec (2 x) = 3

6 sin (x) - 5 cos (x) = 7

sin (x) tan (x) = 1

cos (x) = \frac{1}{2}, 0 \leq x < 2 π