buktikan a. (sin x- cos x)^2=1- 2 sin x cos x b. (cos x + sin x)^2 - (cos x -sin x)^2= 4 sin x cos x tolong bantu bsk uas
Matematika
Mirapramesty
Pertanyaan
buktikan
a. (sin x- cos x)^2=1- 2 sin x cos x
b. (cos x + sin x)^2 - (cos x -sin x)^2= 4 sin x cos x
tolong bantu bsk uas
a. (sin x- cos x)^2=1- 2 sin x cos x
b. (cos x + sin x)^2 - (cos x -sin x)^2= 4 sin x cos x
tolong bantu bsk uas
2 Jawaban
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1. Jawaban CyntiaSianturi23
a. (sinx-cosx)² = 1 - 2sinxcosx
--> (sinx-cosx)²
= sin²x + cos²x -2sinxcosx
= 1 - 2sinxcosx
[TERBUKTI]
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b. (cosx + sinx)² - (cosx-sinx)² = 4sinxcosx
--> (cosx + sinx)² - (cosx-sinx²)
= cos²x + sin²x + 2sinxcosx - (cos²x + sin²x -2sinxcosx)
= 1 + 2sinxcosx - (1 -2sinxcosx)
= 1 + 2sinxcosx - 1 + 2sinxcosx
= 4sinxcosx
[TERBUKTI]
Semoga membantuu :) -
2. Jawaban whongaliem
a) (sin x - cos x)² = 1 - 2.sin x .cos x
.sin² x - 2.sin x .cos x + cos² x = 1 - 2.sin x .cos x
(sin² x + cos² x) - 2.sin x .cos x = 1 - 2.sin x .cos x
1 - 2 .sin x .cos x = 1 - 2.sin x .cos x
( terbukti ...)
b) (cos x + sin x)² - (cos x - sin x)² = 4.sin x .cos x
(cos x + sinx + cos x - sin x) (cos x + sin x - cos x + sin x) = 4.sin x .cos x
( 2 .cos x ) (2 .sin x) = 4.sin x .cos x
4 .cos x .sin x = 4 .sin x .cos x
terbukti ....