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Popular >

verificar (1/2 sin^2(θ))=(1/2 cos(2θ))

Solución

verificar

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

Solución

Falso

Pasos de solución

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

Ambos lados no son iguales

Multiplicar

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

por

θ = 0

\frac{1}{2} sin^{2} (0) = 0

\frac{1}{2} sin^{2} (0)

Utilizar la siguiente identidad trivial:

sin (0) = 0

sin (0)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= 0

= \frac{1}{2} \cdot 0^{2}

Simplificar

= 0

\frac{1}{2} cos (2 \cdot 0) = \frac{1}{2} (Decimal : 0.5)

\frac{1}{2} cos (2 \cdot 0)

Simplificar:

2 \cdot 0 = 0

2 \cdot 0

Aplicar la regla

0 \cdot a = 0

= 0

\frac{1}{2} cos (0) = \frac{cos ( 0 )}{2}

\frac{1}{2} cos (0)

Multiplicar fracciones:

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

= \frac{1 \cdot cos ( 0 )}{2}

Multiplicar:

1 \cdot cos (0) = cos (0)

= \frac{cos ( 0 )}{2}

= \frac{cos ( 0 )}{2}

Utilizar la siguiente identidad trivial:

cos (0) = 1

cos (0)

cos (x)

tabla de valores periódicos con

2 πn

intervalos:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= 1

= \frac{1}{2}

Ambos lados no son iguales

\Rightarrow Falso

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