Nilai [(cos (90 + A) ⋅ tan (180 − A))/(sin (360 − ...

Question

Nilai [(cos (90 + A) ⋅ tan (180 − A))/(sin (360 − A) ⋅ cot (270 − A))] +(sec (90 − A))/(cosec (180 − A)) = ⋯

F. Fauzi · Accepted Answer

Jawaban yang benar adalah 0

Ingat identitas trigonometri,
tanA = sinA/cosA
cosec A = 1/sinA
cos (90+A) = - sinA
tan (180-A) = - tanA
sin (360-A) = - sinA
sec (90-A) = cosecA
cosec (180-A) = cosecA
cot (270-A) = tanA

= [(cos (90 + A) ⋅ tan (180 − A))/(sin (360 − A) ⋅ cot (270 − A))] +(sec (90 − A))/(cosec (180 − A))
= [(- sinA) ⋅ (- tanA)/(- sinA) ⋅ (tanA)] +[(cosecA)/(cosecA)]
= [(sinA.tanA)/(- sinA.tanA)] +[1]
= [-1] +[1]
= 0

Jadi, Nilai [(cos (90 + A) ⋅ tan (180 − A))/(sin (360 − A) ⋅ cot (270 − A))] +(sec (90 − A))/(cosec (180 − A)) adalah 0

Nilai [(cos (90 + A) ⋅ tan (180 − A))/(sin (360 − A) ⋅ cot (270 − A))] +(sec (90 − A))/(cosec (180 − A)) = ⋯

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