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tan(arcsin(1/2)+arccos(-(sqrt(3))/2))

Solución

tan (arcsin (\frac{1}{2}) + arccos (- \frac{3}{2}))

0

Pasos de solución

tan (arcsin (\frac{1}{2}) + arccos (- \frac{3}{2}))

Re-escribir usando identidades trigonométricas:

\frac{tan ( arcsin ( \frac{1}{2} ) ) + tan ( arccos ( - \frac{3}{2} ) )}{1 - tan ( arcsin ( \frac{1}{2} ) ) tan ( arccos ( - \frac{3}{2} ) )}

tan (arcsin (\frac{1}{2}) + arccos (- \frac{3}{2}))

Utilizar la identidad de suma de ángulos:

tan (s + t) = \frac{tan ( s ) + tan ( t )}{1 - tan ( s ) tan ( t )}

= \frac{tan ( arcsin ( \frac{1}{2} ) ) + tan ( arccos ( - \frac{3}{2} ) )}{1 - tan ( arcsin ( \frac{1}{2} ) ) tan ( arccos ( - \frac{3}{2} ) )}

= \frac{tan ( arcsin ( \frac{1}{2} ) ) + tan ( arccos ( - \frac{3}{2} ) )}{1 - tan ( arcsin ( \frac{1}{2} ) ) tan ( arccos ( - \frac{3}{2} ) )}

Re-escribir usando identidades trigonométricas:

tan (arcsin (\frac{1}{2})) = \frac{3}{3}

tan (arcsin (\frac{1}{2}))

Re-escribir usando identidades trigonométricas:

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

Usar la siguiente identidad:

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

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

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

Simplificar

= \frac{3}{3}

Re-escribir usando identidades trigonométricas:

tan (arccos (- \frac{3}{2})) = - \frac{3}{3}

tan (arccos (- \frac{3}{2}))

Re-escribir usando identidades trigonométricas:

tan (arccos (- \frac{3}{2})) = \frac{1 - ( - \frac{3}{2} ) ^{2}}{( - \frac{3}{2} )}

Usar la siguiente identidad:

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

= \frac{1 - ( - \frac{3}{2} ) ^{2}}{( - \frac{3}{2} )}

= \frac{1 - ( - \frac{3}{2} ) ^{2}}{- \frac{3}{2}}

Simplificar

= - \frac{3}{3}

= \frac{\frac{3}{3} - \frac{3}{3}}{1 - \frac{3}{3} ( - \frac{3}{3} )}

Simplificar

= 0

6 cos (10 5^{\circ}) + 6 cos (1 5^{\circ})

6 cos (13 5^{\circ}) - 6 cos (4 5^{\circ})

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\frac{sin ( 1 0 ^{\circ} )}{cos ( 8 0 ^{\circ} )} + \frac{tan ( 2 0 ^{\circ} )}{cot ( 7 0 ^{\circ} )}