Question

Dla α = 60° prawdziwa jest równość:
A. √3sin α + 1/2 = tg 30°
B. sin²α - cos²α= 1
C. cosα + cos(90°-α) = 1/((√3) -1)
D. 2 sinα + cos α = 2/(√(3) +1)

Answer 1

A
√3 sin60° + 1/2 = tg30°
√3 * √3/2 + 1/2 = √3/3
3/2 + 1/2 = √3/3
4/2 = √32/3
2 ≠ √3/3
B
sin²60° -  cos²60° = 1
(√3/2)² - ((1/2)² = 1
3/4 - 1/4 = 1
2/4 ≠ 1

C
cos60° + cos(90° - 60°) = 1/(√3 - 1)
1/2 + sin60° = 1/(√3 - 1)
1/2 + √3/2 = 1/(√3 - 1)
(1 + √3)/2 = 1/(√3 - 1)
(√3 + 1)(√3 - 1) = 2
3 - 1 = 2
2 = 2
L = P

D
2sin60° + cos60° = 2/(√3 + 1)
2 * √3/2 + 1/2 = 2/(√3 + 1)
√3 + 1/2 = 2/(√3 + 1)
2(√3 + 1)/2 = 2/(√3 + 1)
4 = 2(√3 + 1)(√3 + 1) = 2(√3 + 1)² = 2(3 + 2√3 + 1) = 2(4 + 2√3) = 4(2 + √3)
4 ≠ 4(2 + √3)
odp C