16515531 16515531

03-08-2022
Mathematics

contestada

Prove the identity.
tan^5x = tan x (sec² x - 2 sec² x + 1)

Prove the identity tan5x tan x sec x 2 sec x 1 class=

Respuesta :

bunnuika bunnuika

03-08-2022

goal:tan^5x=tanx(sec²x-2sec²x+1)

proof: from l.h.s to r.h.s

tan^5x=(tanx)^5=((tanx)(tan²x)(tan²x))

from trigonometry identity

(tan²x)=sec²x-1

tan^5x=(tanx(sec²x-1)(sec²x-1))

=(tanx(sec^4x-sec²x-sec²x+1))

=(tanx(sec^4x-2sec²x+1))

proved

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