Question

Jika cos(a-b) = ½√3 dan cos a.cos b = ½ dengan sudut a dan b lancip, maka
Cos(a-b)/cos(a+b) =.....

Answer 1

Verified answer

TriGonoMetRi

cos (a - b) = 1/2 √3
cos a cos b + sin a sin b = 1/2 √3
1/2 + sin a sin b = 1/2 √3
sin a sin b = 1/2 (√3 - 1)

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cos (a - b) / cos (a + b)
= 1/2 √3 / cos a cos b - sin a sin b
= 1/2 √3 / (1/2 - 1/2 (√3 - 1))
= 1/2 √3 / (1 - 1/2 √3)
= 1/2 √3 × 2/(2 - √3)
= √3 / (2 - √3)
= √3 (2 + √3) /(2² - (√3)²)
= 3 + 2√3