Jika sin α = 1/ akar 3, maka harga cesecα. tgα adalah ...

Bab Trigonometri
Matematika SMA Kelas X

sin a = 1/√3

cosec a . tan a = (1/sin a) . (sin a/cos a)
cosec a . tan a = 1/cos a
cosec a . tan a = 1/√(1 - sin² a)
cosec a . tan a = 1/√(1 - (1/√3)²)
cosec a . tan a = 1/√(1 - 1/3)
cosec a . tan a = 1/√(2/3)
cosec a . tan a = 1/(√2 : √3)
cosec a . tan a = (√3)/√2
cosec a . tan a = (1/2) √6

sin a = 1/√3

cosec a . tan a
= 1/sin a . sin a/cos a
= 1/cos a
= 1/(√(1 - sin² a)
= 1/(√(1 - (1/√3)²)
= 1/(√1 - 1/3)
= 1/(√(2/3))
= √3 / √2
= 1/2 √6

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