Question

Buktikan
(sin a + cos a)^2 + (sin a - cos a)^2 = 2
Tolong jawab dengan cepat dan benar

Answer 1

(sin a + cos a)² + (sin a - cos a)² = 2

sin²A + cos²A + 2.sin A.cos A = 1
sin²A + cos²A - 2.sin A.cos A = 1

= 1 + 1
= 2

Answer 2

Cara lain
x = sin a + cos a
y = sin a - cos a
x² +y² = 2
(x+y)² - 2(xy) = 2

(sin a+ cos a + sin a - cos a)² - 2(sin a+cos a)(sin a- cos a) = 2
(2 sin a)² - 2(sin² a - cos² a) = 2
4 sin² a - 2 sin² a + 2 cos² a = 2
2 sin² a + 2 cos² a = 2
2 (sin² a + cos² a)= 2
2 (1) = 2
2 = 2
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