Matematika

Pertanyaan

nilai (sin x +cos x) ^2 + (1-tan x) ^2/1 + tan^2 x =
nilai (sin x +cos x) ^2 + (1-tan x) ^2/1 + tan^2 x =

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1 Jawaban

  • = sin²x + cos²x + 2sin x cos x + {(1-tan x)² / sec²x}
    = 1 + 2sin x cos x + {(1 - 2tan x + tan²x) / sec²x)
    = 1 + 2sin x cos x + {(sec²x - 2tan x) / sec²x)
    = {sec²x(1+2sin x cos x) + sec²x - 2tan x} / sec²x
    = (sec²x + 2tan x + sec²x - 2tan x) / sec²x
    = 2sec²x / sec²x
    = 2

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