Matematika Kuis: Buktikan jika . . . .(a.) 2cos²(x) - 1 = 1 - 2sin²(x)(b.) 1 + cos(2x) = sin(2x) · cot(x)(c.) sin(x) = cos(x) · tan(x)

jabaricruickshankulv – April 08, 2023

Kuis:

Buktikan jika . . . .

(a.) 2cos²(x) - 1 = 1 - 2sin²(x)

(b.) 1 + cos(2x) = sin(2x) · cot(x)

(c.) sin(x) = cos(x) · tan(x)

Jawab:

(a) 2 cos^2(x) - 1 = 1 - 2 sin^2(x)
2 sin^2(x) + 2 cos^2(x)= 1+1
2(sin^2(x)+ cos^2(x)= 2
2(1)= 2
2= 2

(b) 1 + cos (2x) = sin 2x . cot x
1 + cos^2(x)-sin^2(x)= 2 sin x cos x . (cos x/sin x)
(sin^2(x)+cos^2(x)) + cos^2(x)-sin^2(x)= 2cos^2(x)
2 cos^2(x)= 2cos^2(x)

(c) sin (x) = cos (x) . tan(x)
sin (x)= cos (x) . sin(x)/cos(x)
sin(x)= sin(x)

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