Bentuk (cos 135 + cos 75) senilai dengan

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Bentuk (cos 135 + cos 75) senilai dengan

cos 135+cos 75\ =cos (90+45)+cos (45+30)\ =[cos 90.cos 45 -sin 90.sin 45]+[cos 45.cos 30-sin 45.sin 30]\\ =[0. frac{1}{2} sqrt{2}-1.frac{1}{2} sqrt{2} ]+[frac{1}{2} sqrt{2}.frac{1}{2} sqrt{3}-frac{1}{2} sqrt{2}.frac{1}{2}]\\ =[0-frac{1}{2} sqrt{2}]+[frac{1}{4} sqrt{6}-frac{1}{4} sqrt{2}]\\ =-frac{1}{2} sqrt{2}+frac{1}{4} sqrt{6}-frac{1}{4} sqrt{2}\\ =frac{1}{4} sqrt{6}-frac{1}{2} sqrt{2}-frac{1}{4} sqrt{2}\
=frac{1}{4} sqrt{6}-frac{3}{4} sqrt{2}\

Cos 135 + cos 75
= 2 cos 1/2 (135 + 75) cos 1/2 (135 – 75)
= 2 cos 1/2 x 210 cos 1/2 x 60
= 2 cos 105 cos 30
= 2 . (1/4 √2 – 1/4 √6) . 1/2 √3
= 1/4 √6 – 1/4 √18
= 1/4 √6 – 3/4 √2

kalo ngga salah..