Question

Materi : Identitas Trigonometri
Kelas : XI SMA K.13 Revisi
Bab 1 : Persamaan Trigonometri

Buktikanlah Indentitas Berikut Ini :
/ = per

◆> 1-tan^2 θ / 1+tan^2 θ = cos^2 θ - sin^2 θ
◆> (sin θ + cos θ)^2 + (sin θ - cos θ)^2 = 2
◆> 1/1+cos θ + 1/1-cos θ = 2csc^2 θ
◆> csc^2 θ (sec^2 θ - tan^2 θ ) - 1 = cot^2 θ
◆> 1/1-sinx + 1/1+sinx = 2sec^2 x

Please , Solve The Question
"Complete Manner , I'll give best Solution" :D

Answer 1

Verified answer

▶
(1 - tan² x) / (1 + tan² x)
= (cos² x - sin² x) / (cos² x . sec² x)
= cos 2x / 1
= cos² x - sin² x
TerBukTi

▶
(sin x + cos x)² + (sin x - cos x)²
= (sin² x + cos² x) + 2sin x cos x + (sin² x + cos² x) - 2sin x cos x
= 1 + 0 + 1
= 2
Terbukti

▶
1/(1 - sin x) + 1/(1 + sin x)
samakan penyebut
((1 + sin x) + (1 - sin x)) / (1 - sin² x)
= 2/cos² x
= 2 sec² x
TerBukTi

▶
csc² x (sec² x - tan² x) - 1
= csc² x × 1 - 1
= csc² - 1
= (1 - sin² x)/sin² x
= cos² x / sin² x
= cot² x
Terbukti


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tetha = x