segitiga ABC siku-siku di C jika sin A = k , maka tan( A - B )=... Mohon bantuanya yaa terima kasih

TriGonoMetRi

∆ABC siku di C
sin A = cos B = k

BC/AB = k/1
AC = √(AB² - BC²)
AC = √(1 - k²)

cos A = sin B = AC/AB = √(1 - k²)

tan A tan B
= sin A/cos A . sin B/cos B
= cos B/sin B . sin B/cos B
= 1

tan A - tan B
= k/√(1 - k²) - √(1 - k²) /k
= (k² - (1 - k²)) / k√(1 - k²)
= (2k² - 1) / k√(1 - k²)

tan (A - B)
= (tan A - tan B) / (1 + tan A tan B)
= 1/2 . (2k² - 1) / k√(1 - k²) ✔