verificar (1-cos(θ))(1+sec(θ))=sec(θ)-cos(θ)

Solución

verificar

(1 - cos (θ)) (1 + sec (θ)) = sec (θ) - cos (θ)

Verdadero

Pasos de solución

(1 - cos (θ)) (1 + sec (θ)) = sec (θ) - cos (θ)

Manipular el lado derecho

(1 - cos (θ)) (1 + sec (θ))

Expresar con seno, coseno

= \frac{( 1 + cos ( θ ) ) ( 1 - cos ( θ ) )}{cos ( θ )}

Expandir

(1 + cos (θ)) (1 - cos (θ)) : 1 - cos^{2} (θ)

= \frac{1 - cos ^{2} ( θ )}{cos ( θ )}

Manipular el lado izquierdo

sec (θ) - cos (θ)

Expresar con seno, coseno

= \frac{1 - cos ^{2} ( θ )}{cos ( θ )}

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

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

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

sin (2 x) cot (x) = 2 - 2 sin^{2} (x)

tan^{2} (x) csc^{2} (x) cot^{2} (x) sin^{2} (x) = 1

sec (x) cot (x) sin (x) = 1