Для начала найдем значение cos(a) по формуле:
sin^2(a) + cos^2(a) = 1
(√5/21)^2 + cos^2(a) = 15/441 + cos^2(a) = 1cos^2(a) = 1 - 5/441cos^2(a) = 436/441cos(a) = ±√(436/441)cos(a) = ±√436 / √441cos(a) = ± √(4x109) / 21cos(a) = ± 2√109 / 21
Так как pi/2 ≤ a ≤ pi, cos(a) < 0cos(a) = -2√109 / 21
Теперь найдем √(21)cos(a):
√21cos(a) = √21 * (-2√109 / 21)√21cos(a) = -2√109
Итак, √21*cos(a) = -2√109.
Для начала найдем значение cos(a) по формуле:
sin^2(a) + cos^2(a) = 1
(√5/21)^2 + cos^2(a) = 1
5/441 + cos^2(a) = 1
cos^2(a) = 1 - 5/441
cos^2(a) = 436/441
cos(a) = ±√(436/441)
cos(a) = ±√436 / √441
cos(a) = ± √(4x109) / 21
cos(a) = ± 2√109 / 21
Так как pi/2 ≤ a ≤ pi, cos(a) < 0
cos(a) = -2√109 / 21
Теперь найдем √(21)cos(a):
√21cos(a) = √21 * (-2√109 / 21)
√21cos(a) = -2√109
Итак, √21*cos(a) = -2√109.