Nilai cos 195° - sin 15° adalah

Nilai cos 195° – sin 15° adalah

Jawab:

cos 195° – sin 15° = $-frac{1}{2} sqrt{6}$

Penjelasan dengan langkah-langkah:

cos (a+b)=cos a. cos b – sin a. sin b

cos 195 = cos (150+45)

= cos 150.cos 45 – sin 150. sin 45

= $-frac{1}{2}sqrt{3}$ . $frac{1}{2}sqrt{2}$ – $frac{1}{2}$ . $frac{1}{2}sqrt{2}$

= $-frac{1}{4}sqrt{6}$ $-frac{1}{4} sqrt{2}$

sin (a-b) = sin a. cos b – cos a. sin b

sin 15 = sin (45-30)

= sin 45. cos 30 – cos 45. sin 30

= $frac{1}{2}sqrt{2}$ . $frac{1}{2} sqrt{3}$ – $frac{1}{2}sqrt{2}$ . $frac{1}{2}$

= $frac{1}{4}sqrt{6}$ $-frac{1}{4} sqrt{2}$

cos 195 – sin 15 = $-frac{1}{4}sqrt{6}$ $-frac{1}{4} sqrt{2}$ $-($ $frac{1}{4}sqrt{6}$ $-frac{1}{4} sqrt{2}$ $)$

= $-frac{2}{4} sqrt{6}$

= $-frac{1}{2} sqrt{6}$

semoga membantu:)