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verificar (1+cos(2x))/2 =cos^2(x)

Solución

verificar

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

Verdadero

Pasos de solución

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

Manipular el lado derecho

\frac{1 + cos ( 2 x )}{2}

Re-escribir usando identidades trigonométricas

\frac{1 + cos ( 2 x )}{2}

Utilizar la identidad trigonométrica del ángulo doble:

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

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

Simplificar

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

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

1 + 2 cos^{2} (x) - 1 = 2 cos^{2} (x)

1 + 2 cos^{2} (x) - 1

Agrupar términos semejantes

= 2 cos^{2} (x) + 1 - 1

1 - 1 = 0

= 2 cos^{2} (x)

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

Dividir:

\frac{2}{2} = 1

= cos^{2} (x)

= cos^{2} (x)

= cos^{2} (x)

Se demostró que ambos lados pueden tomar la misma forma

\Rightarrow Verdadero

\frac{tan ( x )}{1 + sec ( x )} = - cot (x) + csc (x)

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

cos (3 x) = 4 (cos (x))^{3} - 3 cos (x)

cos (θ) = sin (\frac{π}{2} + θ)

1 - 8 sin^{2} (θ) cos^{2} (θ) = cos (4 θ)