Nilai dari sin 15 – cos 15/ tan 15 adalah ​

sin 15° – cos 15°/tan15°

~> sin 15° = sin (45° – 30°)

= sin45.cos30 – sin30.cos45

= √2/2.√3/2 – 1/2.√2/2

= √6/4 – √2/4 ~ (√6 – √2)/4 ✓

~> cos 15° = cos (45° – 30°)

= cos45.cos30 + sin45.sin30

= √2/2.√3/2 + √2/2.1/2

= √6/4 + √2/4 ~ (√6 + √2)/4 ✓

~> tan 15° = tan (45° – 30°)

= (tan45 – tan30)/1 + tan45.tan30

= (1 – 1/√3)/1 + 1/√3

= (√3 – 1)/√3/(√3 + 1)/√3

= (√3 – 1)/(√3 + 1) ✓

~> [(√6 – √2)/4 – (√6 + √2)/4]/[(√3 – 1)/(√3 + 1)]

-(√3 + 1)√2/2(√3 – 1)

(√6 + √2)/(2 – 2√3) ✓✓