Popular >

verificar 1/(sin(θ)cos(θ))=sec(θ)csc(θ)

Solución

verificar

\frac{1}{sin ( θ ) cos ( θ )} = sec (θ) csc (θ)

Verdadero

Pasos de solución

\frac{1}{sin ( θ ) cos ( θ )} = sec (θ) csc (θ)

Manipular el lado izquierdo

sec (θ) csc (θ)

Expresar con seno, coseno

csc (θ) sec (θ)

Utilizar la identidad trigonométrica básica:

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

= \frac{1}{sin ( θ )} sec (θ)

Utilizar la identidad trigonométrica básica:

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

= \frac{1}{sin ( θ )} \cdot \frac{1}{cos ( θ )}

Simplificar

\frac{1}{sin ( θ )} \cdot \frac{1}{cos ( θ )} : \frac{1}{sin ( θ ) cos ( θ )}

\frac{1}{sin ( θ )} \cdot \frac{1}{cos ( θ )}

Multiplicar fracciones:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{sin ( θ ) cos ( θ )}

Multiplicar los numeros:

1 \cdot 1 = 1

= \frac{1}{sin ( θ ) cos ( θ )}

= \frac{1}{sin ( θ ) cos ( θ )}

= \frac{1}{cos ( θ ) sin ( θ )}

= \frac{1}{sin ( θ ) cos ( θ )}

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

sec (x) \frac{tan ( x )}{sin ( x )} = sec^{2} (x)

\frac{1 + tan ^{2} ( θ )}{csc ^{2} ( θ )} = tan^{2} (θ)

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

sin (3 θ) + sin (θ) = 2 sin (θ) cos (θ)