Buktikanlah identitas trigonometri berikut cos^4 x (1-tan^4 x) = cos^2x - sin^2x
Matematika
Michael151200
Pertanyaan
Buktikanlah identitas trigonometri berikut cos^4 x (1-tan^4 x) = cos^2x - sin^2x
1 Jawaban
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1. Jawaban Anonyme
Kelas 11 Matematika
Bab Trigonometri Lanjut
^ = pangkat
cos^4 x . (1 - tan^4 . x)
= cos^4 x - cos^4 x . tan^4 x
= cos^4 x - (cos^4 x . sin^4 . x/cos^4 x)
= cos^4 x - sin^4 x
= (cos² x + sin² x) . (cos² x - sin² x)
= 1 . (cos² x - sin² x)
= cos² x - sin² x