Question

prove tan A/sec A -1 + tan A / sec A +1 = 2 cosec A​

Answer 1

Faça M.M.C. e distribua:

⇒

tan (A) . [sec (A) +1] + tan (A) . [ sec (A) -1 ] = 2 cossec (A) . [sec ² (A) - 1]

Use a Relação Trigonométrica Auxiliar: sec ² x = tan ² x + 1

⇒

tan (A) . [sec (A) +1] + tan (A) . [ sec (A) -1 ] = 2 cossec (A) . tan ² (A)

Coloque tan (A) em evidência:

⇒

tan (A) . [ sec (A) + 1 + sec (A) - 1 ] = 2 cossec (A) . tan ² (A)

Desenvolva simplificando:

⇒

2 sec (A) = 2 cossec (A) . tan (A)

sec (A) = cossec (A) . tan (A)

sec (A) / cossec (A) = tan (A)

tan (A) = tan (A)