Cos 105\xb0 + Cos 195\xb0 2013 Cos 15\xb0 + Cos 75\xb0

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Cos 105° + Cos 195° – Cos 15° + Cos 75°​

Jawab:

trigonometri

cos (180+ a) = – cos a

cos (180- a) =  - cos a

nilai  

cos 105 + cos 195    - cos 15  +cos 75 =

= cos (180-75) + cos (180+15) – cos 15 + cos 75

= – cos 75 –  cos 15 – cos 15 + cos 75

= – 2 cos 15

=  -2  cos (45 – 30)

= – 2 { cos 45 cos 30 + sin 45 sin  30}

=  -2  { 1/2 √2 . 1/2√3  + 1/2√2 .1/2)

= – 2 { 1/4 √6 – 1/4 √2)

= – 2 (1/4)(√6 – √2)

=  -1/2 (√6 – √2)


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