a. sina = 1 – cos²a/1 + sina
b. cos²a/1 + sina + cos²a/1-sina = 2
c. 1 – tg²a/1 + tg²a = cos²a – sin²a
Buktikan identitas trigonometri
a]
sin A = (1 – cos^2 A)/(1 + sin A)
(sin^2 A)/sin A = (1 – cos^2 A)/(1 + sin A)
(1 – cos^2 A)/sin A = (1 – cos^2 A)/(1 + sin A)
(TIDAK TERBUKTI)
b]
cos^2 A/(1 + sin A) + cos^2 A/(1 – sin A) = 2
(1 – sin^2 A)/(1 + sin A) + (1 – sin^2 A)/(1 – sin A) = 2
[(1 – sin^2 A)(1 – sin A) + (1 – sin^2 A)(1 + sin A)]/(1 + sin A)(1 – sin A) = 2
[(1 – sin A – sin^2 A + sin^3 A) + (1 + sin A – sin^2 A – sin^3 A)]/(1 – sin^2 A) = 2
(1 – sin A – sin^2 A + sin^3 A + 1 + sin A – sin^2 A – sin^3 A)/(1 – sin^2 A) = 2
(2 – 2sin^2 A)/(1 – sin^2 A) = 2
2(1 – sin^2 A)/(1 – sin^2 A) = 2
2 = 2
(TERBUKTI)
c]
(1 – tg^2 A)/(1 + tg^2 A) = cos^2 A – sin^2 A
(1 – sin^2 A/cos^2 A)/(1 + sin^2 A/cos^2 A) = cos^2 A – sin^2 A
(cos^2 A/cos^2 A – sin^2 A/cos^2 A)/(cos^2 A/cos^2 A + sin^2 A/cos^2 A) = cos^2 A – sin^2 A
[(cos^2 A – sin^2 A)/cos^2 A]/[(cos^2 A + sin^2 A)/cos^2 A] = cos^2 A – sin^2 A
[(cos^2 A – sin^2 A)/cos^2 A] × [cos^2 A/(cos^2 A + sin^2 A)] = cos^2 A – sin^2 A
(cos^2 A – sin^2 A)/(cos^2 A + sin^2 A) = cos^2 A – sin^2 A
(cos^2 A – sin^2 A)/1 = cos^2 A – sin^2 A
cos^2 A – sin^2 A = cos^2 A – sin^2 A
(TERBUKTI)