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(tan^2(x)(1+cot^2(x)))/(sec(x))=cos(x)

Solución

\frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) )}{sec ( x )} = cos (x)

Solución

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

Pasos de solución

\frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) )}{sec ( x )} = cos (x)

Restar

cos (x)

de ambos lados

\frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) )}{sec ( x )} - cos (x) = 0

Simplificar

\frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) )}{sec ( x )} - cos (x) : \frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) ) - cos ( x ) sec ( x )}{sec ( x )}

\frac{tan ^{2} ( x ) ( 1 + cot ^{2} ( x ) ) - cos ( x ) sec ( x )}{sec ( x )} = 0

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

tan^{2} (x) (1 + cot^{2} (x)) - cos (x) sec (x) = 0

Re-escribir usando identidades trigonométricas

1 + tan^{2} (x) - 1 = 0

Mover

1

al lado derecho

tan^{2} (x) - 1 = - 1

Mover

1

al lado derecho

tan^{2} (x) = 0

Aplicar la regla

x^{n} = 0 \Rightarrow x = 0

tan (x) = 0

Soluciones generales para

tan (x) = 0

x = 0 + πn

Resolver

x = 0 + πn : x = πn

x = πn

Siendo que la ecuación esta indefinida para:

πn

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

Ejemplos populares

4cos^2(x)tan(x)-tan(x)=0

4 cos^{2} (x) tan (x) - tan (x) = 0

sin(2x)+sin^2(x)+cos^2(x)=0

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

csc(x)= 1/(cos(x))

csc (x) = \frac{1}{cos ( x )}

csc(θ)=(1.201)

csc (θ) = (1.201)

3cos(θ)+2=5sec(θ),0<= θ<2pi

3 cos (θ) + 2 = 5 sec (θ), 0 \leq θ < 2 π