Question

Nilai dari sin 15°(cos 105° – sin 75°) = .....​

Answer 1

sin 15° (cos 105° - sin 75°)

= sin 15° ( ¼ (√2 - √6) - ¼ (√6 + √2) )

= ¼ (√6 - √2) ( ( ¼ (√2 - √6) - ¼ (√6 + √2) )

= ¼ (√6 - √2) ( ( (√2 - √6) / 4 ) - ( (√6 + √2) / 4 )

= ¼ (√6 - √2) ( - 2√6 / 4 )

= ( (√6 - √2) / 4) ( - √6 / 2 )

= ( - √36 + √12 ) / 8

= ( - 6 + 2√3 ) / 8

= ( - 3 + √3 ) / 4

= ( √3 - 3 ) / 4