计算 \((\sin(\dfrac{\pi}{4}) + \cos(\dfrac{\pi}{4})) \times \tan(\dfrac{\pi}{4}) =\)
Compute \((\sin(\dfrac{\pi}{4}) + \cos(\dfrac{\pi}{4})) \times \tan(\dfrac{\pi}{4}) =\)
Вычислите \((\sin(\dfrac{\pi}{4}) + \cos(\dfrac{\pi}{4})) \times \tan(\dfrac{\pi}{4}) =\)
Решение
Значения тригонометрических функций: \(\sin\dfrac{\pi}{4} = \dfrac{\sqrt{2}}{2}\), \(\cos\dfrac{\pi}{4} = \dfrac{\sqrt{2}}{2}\), \(\tan\dfrac{\pi}{4} = 1\).
Сумма синуса и косинуса: \(\dfrac{\sqrt{2}}{2} + \dfrac{\sqrt{2}}{2} = \sqrt{2}\).
Умножаем на тангенс: \(\sqrt{2} \times 1 = \sqrt{2}\).
Ответ: C.