Question

Buktikan identitas trigonometri berikut :

Answer 1

1. Coba di cek soalnya dah benar belum no 1 karena no 1 kalau soalnya kayak
(sin A + cos A) / (sin A + cos A)  + (sin A - cos A) / ( sin A - cos A) = 1 + 1 = 2

2. (1 + tan² A) ( 1 + sin A) (1 - sin A) = (cos²A/cos²A + sin²A/cos²A) ( 1 - sin²A)
 = (1 / cos²A) (cos²A) = 1 (terbukti)

3. (sin A + sec A)² + (cos A + cos A)²
= (sin²A + 2 sin A sec A + sec² A) + (2 cosA)²
= (sin²A + 2 tanA + sec² A) + 4 cos²A
= sin ²A + 4cos²A + 2 tan A + sec²A
= 1 + 3 cos²A + 2 tan A + sec²A
Cek juga soal no 3 dah benar belum

Answer 2

1. - awal2 samakan penyebut : (sin A + cos A) *(sin A - cos A)
                             penyebut = sin^2(A) - cos^2(A)
penyebut dapat dirubah menjadi = (1 - cos^2(A)) - cos^2(A)
                        bukti penyebut  = 1 -2cos^2(A)
 - Pembilang = sin^2(A) - cos^2(A) + sin^2(A) - cos^2(A)
                   = 2sin^2(A) - 2(cos^2(A)) = 2 (sin^2(A) - cos^2(A))
                  = 2(1-cos^2(A)-cos^2(A)) = 2(1 - 2cos^2(A))
hasil total hasil = 2(1- 2cos^2(A))/(1-2cos^2(A)) = 2
               hasil = 2
2. - uraikan   :1 +tan^2(A) = (cos^2(A) +sin^2(A))/cos^2(A)
      kalikan  : (1+sin^2(A))(1-sin^2(A)) = 1 - sin^2(A) = cos^2(A)
Operasikan secara total : (cos^2(A) + sin^2(A))/cos^2(A) * cos^2(A)
                    hasil = cos^2(A) +sin^2(A) =1
                    hasil = 1
3. kalikan : (cos(A) + cos(A))^2 = (2 cos(A))^2 = 4 (cos^2(A)) = 4(1 - sin^2(A))
    samakan & urai : (sin(A) +sec(A))^2 = (sin (A) + 1/sin(A))^2 
                             = ((sin^2(A) + 1)/sin(A))^2
                             = (((sin^2(A) + (sin^2(A) + cos^2(A) )) sin(A))^2
                             = ((2 sin^2(A) + (1 -sin^2(A)))/sin(A))^2
                             = ((sin^2(A) +1)/sin(A))^2 = (sin^4(A) + 2 sin^2(A) +1)/sin(A)
         operasi total  = (sin^4(A) +2 sin^2(A) +1 +4 Sin(A) -4 sin^3(A))/sin (A)
                     hasil = sin^3(A) +2 Sin(A) + sec(A) +4 - sin^2(A)

jadi klo dilihat pembuktian yg tertulis di soal terutama nomor 1 & 3 tidak sama, namun saya jamin yg saya kerjakan betul dan yg nomor