Question

Tolong dijawab yah !!

Answer 1

Verified answer

`15
(1 + cot² B)/ (cot B sec² B) = cot B
ruas kliri
(1 + cot² B)/ (cot B sec² B) =
= csc² B/ { cot B sec² B)
= ( 1/sin² B) / ( cos B/sin B . 1/(cos² B)}
= (1/sin² B ) ( 1/ sin B . cos B)
= (1/ sin² B) (sin B cos B)
= (cos B)/(sin B)
= cot B

16
sin⁴ a (cot⁴ a -1) =  2 cos² a - 1
ruas kiri
sin⁴a (cot⁴a - 1) =
= sin⁴ a ( cos⁴ a/sin⁴ a  - 1)
= cos⁴ a - sin⁴ a
= (cos² a + sin² a)(cos² a - sin² a)
= 1 (cos² a - sin² a)
 = cos² a - (1 - cos² a)
= 2 cos² a - 1

17.
(tan  a - 1)/(tan a +1). (sin a + cos a)/(sin a - cos a) = 1
ruas kiri
(tan a -1)/(tan a +1). (sin a + cos a)/(sin a - cos a)=
..
tan a - 1 = (sin a/cos a -1)= (sin a - cos a)/cos a
tan a + 1 = (sin a /cos a +1) = (sin a + cos a )/ cos a
tan a - 1/ tan a+1 =  (sin a - cos a )/(sin a + cos a)
.
{(tan a -1)/(tan a +1)} {(sin a + cos a)/(sin a - cos a)}=
= {(sin a - cos a)/ (sin a + cos a)}{sin a + cos a)/(sin a - cos a)}
= (sin a -cos a)(sin a + cos a)/ (sin a +cos a)(sin a - cos a)
= 1.

Answer 2

Verified answer

Kelas : XI
Pelajaran : Matematika
Kategori : Pembuktian Identitas Trigonometri

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