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Question Number 208437 by efronzo1 last updated on 16/Jun/24

Answered by som(math1967) last updated on 16/Jun/24

 a=sin84+cos66  ⇒a=sin84+sin24  ⇒a=2sin54cos30   ∴a=2×(((√5)+1)/4)×((√3)/2)=(((√3)((√5)+1))/4)  b=sin48−sin12  ⇒b=2sin18.cos30=(((√3)((√5)−1))/4)  ab=((3(5−1))/(4×4))=(3/4)   (a/b)=(((√5)+1)/( (√5)−1))  ⇒((a+b)/(a−b))=((2(√5))/2)=(√5)   (((a+b)/(a−b)))^(8ab) =5^((1/2)×8×(3/4)) =5^3

a=sin84+cos66a=sin84+sin24a=2sin54cos30a=2×5+14×32=3(5+1)4b=sin48sin12b=2sin18.cos30=3(51)4ab=3(51)4×4=34ab=5+151a+bab=252=5(a+bab)8ab=512×8×34=53

Commented by efronzo1 last updated on 16/Jun/24

 = 5^3

=53

Commented by som(math1967) last updated on 16/Jun/24

yes

yes

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