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Popular >

-sin(x)-2cot(x)+5csc(x)=0

Solución

- sin (x) - 2 cot (x) + 5 csc (x) = 0

Sin soluci \overset{o}{ˊ} n para x \in R

Pasos de solución

- sin (x) - 2 cot (x) + 5 csc (x) = 0

Expresar con seno, coseno

- sin (x) - 2 \cdot \frac{cos ( x )}{sin ( x )} + 5 \cdot \frac{1}{sin ( x )} = 0

Simplificar

- sin (x) - 2 \cdot \frac{cos ( x )}{sin ( x )} + 5 \cdot \frac{1}{sin ( x )} : \frac{- sin ^{2} ( x ) - 2 cos ( x ) + 5}{sin ( x )}

\frac{- sin ^{2} ( x ) - 2 cos ( x ) + 5}{sin ( x )} = 0

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

- sin^{2} (x) - 2 cos (x) + 5 = 0

Sumar

2 cos (x)

a ambos lados

- sin^{2} (x) + 5 = 2 cos (x)

Elevar al cuadrado ambos lados

(- sin^{2} (x) + 5)^{2} = (2 cos (x))^{2}

Restar

(2 cos (x))^{2}

de ambos lados

(- sin^{2} (x) + 5)^{2} - 4 cos^{2} (x) = 0

Factorizar

(- sin^{2} (x) + 5)^{2} - 4 cos^{2} (x) : (- sin^{2} (x) + 5 + 2 cos (x)) (- sin^{2} (x) + 5 - 2 cos (x))

(- sin^{2} (x) + 5 + 2 cos (x)) (- sin^{2} (x) + 5 - 2 cos (x)) = 0

Resolver cada parte por separado

- sin^{2} (x) + 5 + 2 cos (x) = 0 or - sin^{2} (x) + 5 - 2 cos (x) = 0

- sin^{2} (x) + 5 + 2 cos (x) = 0 :

Sin solución

- sin^{2} (x) + 5 - 2 cos (x) = 0 :

Sin solución

Combinar toda las soluciones

Sin soluci \overset{o}{ˊ} n

Verificar las soluciones sustituyendo en la ecuación original

Sin soluci \overset{o}{ˊ} n para x \in R

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

cos (x) = \frac{π}{3}

\frac{sec ^{2} ( x )}{2} = 2 cos^{2} (x)

arctan (t) = 0

sin (\frac{x}{2}) = - 1