Question

Tolong dijawab yah !!

Answer 1

Verified answer

18) 1/(sec x - tan x)
= 1/(1/(cos x) - (sin x)/(cos x))
= 1/[(1 - sin x)/(cos x)]
= (cos x) / (1 - sin x)
= (cos x)/(1 - sin x) . (1 + sin x)/(1 + sin x)
= cos x (1 + sin x) / (1 - sin^2 x)
= cos x (1 + sin x) / (cos^2 x)
= (1 + sin x) / (cos x)
= 1/(cos x) + (sin x)/(cos x)
= sec x + tan x

19) (sin^2 a - sin^2 b)/(cos^2 a cos^2 b)
= (sin^2 a)/(cos^2 a cos^2 b) - (sin^2 b)/(cos^2 a cos^2 b)
= (sin^2 a)/(cos^2 a) . 1/(cos^2 b) - (sin^2 b)/(cos^2 b) . 1/(cos^2 b)
= tan^2 a . sec^2 b - tan^2 b . sec^2 a
= tan^2 a (1 + tan^2 b) - tan^2 b (1 + tan^2 a)
= tan^2 a + tan^2 a tan^2 b - tan^2 b - tan^2 a tan^2 b
= tan^2 a - tan^2 b

^ = pangkat

Answer 2

Verified answer

Kelas : XI
Pelajaran : Matematika
Kategori : Pembuktian Identitas

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