Matematika

Pertanyaan

pembuktian bahwa :
tan2 x ÷ 1 + sec x = sec x - 1
keterangan:
tan2 x = tangen kuadrat x

1 Jawaban

  • Kelas 10 Matematika
    Bab Trigonometri

    tan² x + 1 = sec² x
    tan² = sec² x - 1
    - tan² x = 1 - sec² x
    1 - sec² x = - tan² x

    ****************************************************************

    tan² x / (1 + sec x)
    = tan² x/(1 + sec x) . (1 - sec x)/(1 - sec x)
    = tan² x . (1 - sec x)/(1² - sec² x)
    = tan² x . (1 - sec x) / (- tan² x)
    = - ( 1 - sec x)
    = sec x - 1

    Terbukti

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