bonjour
ce sont des "égalités"
a)
(cos x + sin x)² = on développe (a + b)² = ...
cos²x + 2 cos x sin x + sin²x =
cos²x + sin²x + 2 cos x sin x =
(cos²x + sin²x) + 2 cos x sin x = [cos²x + sin²x = 1 ]
1 + 2 cos x sin x
b)
tan a = sin a/cos a
tan²a = sin²a / cos²a
1/tan²a = cos²a / sin²a
1 + 1/tan²a = 1 + cos²a/sin²a
= sin²a/sin²a + cos²a/sin²a
= (sin²a + cos²a) / sin²a
= 1/sin²a
c)
(x² - √2 x + 1)(x² + √2 x + 1) =
[ (x² + 1) - √2 x) ] [(x² + 1) + √2 x ] = [ (a - b)(a + b) = ... ]
(x² + 1)² - (√2 x)² =
x⁴ + 2x² + 1 - 2x² =
x⁴ + 1
