PEMBAHASAN

Trigonometri

Jumlah dan Selisih Dua Sudut

tan (a + b) = (tan a + tan b)/(1 - tan a tan b)

tan 75°

= tan (30° + 45°)

= (tan 30° + tan 45°)/(1 - tan 30° tan 45°)

= (1/√3 + 1)/(1 - 1/√3 . 1)

= (1 + √3) / (√3 - 1)

= (1 + √3)²/(3 - 1)

= (4 + 2√3)/2

= 2 + √3

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sin (a + b) = sin a cos b + cos a sin b

sin 105°

= sin (60° + 45°)

= sin 60° cos 45° + cos 60° sin 45°

= 1/2 √3 × 1/2 √2 + 1/2 × 1/2 √2

= 1/4 (√6 + √2)

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cos (a + b) = cos a cos b - sin a sin b

cos 105°

= cos (60° + 45°)

= cos 60° cos 45° - sin 60° sin 45°

= 1/2 × 1/2 √2 - 1/2 √3 × 1/2 √2

= 1/4 (√2 - √6)

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cara 1

tan 105°

= tan (180° - 75°)

= - tan 75°

= -(2 + √3)

= -2 - √3

cara 2

tan 105°

= tan (60° + 45°)

= (tan 60° + tan 45°)/(1 - tan 60° tan 45°)

= (√3 + 1)/(1 - √3 . 1)

= (√3 + 1)²/(1 - 3)

= (4 + 2√3)/(-2)

= -2 - √3