Matematika

Pertanyaan

Tolong yah tunjukan bahwa :
A. (sin a - cos a)^2 = 1 - 2sina.cos
B. tan x.sin x + cos x = sec x
Tolong yah tunjukan bahwa : A. (sin a - cos a)^2 = 1 - 2sina.cos B. tan x.sin x + cos x = sec x

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1 Jawaban

  • identitas trigonometri :
    sin² a + cos² a = 1

    A.
    (sin a - cos a)² = 1 - 2.sin a.cos a
    sin²a + cos²a - 2.sin a.cos a = 1 - 2.sin a.cos a
    1 - 2.sin a.cos a = 1 - 2.sin a.cos a
    (TERBUKTI)

    B.
    tan x.sin x + cos x = sec x
    (sin x/cos x).sin x + cos x = sec x
    sin²x/cos x + cos x = sec x
    (sin²x + cos²x)/cos x = sec x
    1/cos x = sec x
    sec x = sec x
    (TERBUKTI)

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