sin(20)+cos(40)-sin(160)+cos(140)

Solución

sin (2 0^{\circ}) + cos (4 0^{\circ}) - sin (16 0^{\circ}) + cos (14 0^{\circ})

0

Pasos de solución

sin (2 0^{\circ}) + cos (4 0^{\circ}) - sin (16 0^{\circ}) + cos (14 0^{\circ})

Re-escribir usando identidades trigonométricas:

sin (2 0^{\circ}) = sin (16 0^{\circ})

sin (2 0^{\circ})

Utilizar la identidad trigonométrica básica:

sin (x) = sin (18 0^{\circ} - x)

= sin (18 0^{\circ} - 2 0^{\circ})

Simplificar

= sin (16 0^{\circ})

= sin (16 0^{\circ}) + cos (4 0^{\circ}) - sin (16 0^{\circ}) + cos (14 0^{\circ})

Simplificar

= cos (4 0^{\circ}) + cos (14 0^{\circ})

Re-escribir usando identidades trigonométricas:

cos (14 0^{\circ}) = - cos (4 0^{\circ})

cos (14 0^{\circ})

Utilizar la identidad trigonométrica básica:

cos (x) = - cos (18 0^{\circ} - x)

= - cos (18 0^{\circ} - 14 0^{\circ})

Simplificar

= - cos (4 0^{\circ})

= cos (4 0^{\circ}) - cos (4 0^{\circ})

Simplificar

= 0

cos^{2} (5 0^{\circ}) - sin^{2} (5 0^{\circ})

sin (30 0^{\circ} + 4 5^{\circ})

\frac{1 - sin ( 3 2 ^{\circ} )}{1 + sin ( 3 2 ^{\circ} )}

arcsin (sin (\frac{9}{4}))

arccos (- \frac{8}{17})