Question

Sin3x/sinx+cos3x/cosx если x=pi/6

Answer 1

Ответ:

Для решения этого уравнения мы можем подставить значение x = π/6 и заменить функции с помощью тригонометрических тождеств:

sin(3π/6) / sin(π/6) + cos(3π/6) / cos(π/6)

Упрощая это уравнение, мы получаем:

sin(π/2) / sin(π/6) + cos(π/2) / cos(π/6)

Так как sin(π/2) = 1 и cos(π/2) = 0, мы можем дальше упростить это уравнение:

1 / (1/2) + 0 / (√3/2) = 2 + 0 = 2

Таким образом, sin(3x)/sin(x) + cos(3x)/cos(x) при x = π/6 равно 2

Answer 2

To evaluate the expression

(sin(3x) / sin(x)) + (cos(3x) / cos(x))

at x = π/6, we can substitute the value of x and simplify the expression. Let's begin:

Let's first substitute x = π/6 into the expression:

(sin(3 * (π/6)) / sin(π/6)) + (cos(3 * (π/6)) / cos(π/6))

Now, simplify the trigonometric functions:

(sin(π/2) / (1/2)) + (cos(π/2) / (√3/2))

sin(π/2) is equal to 1, and cos(π/2) is equal to 0:

(1 / (1/2)) + (0 / (√3/2))

Reciprocal of 1/2 is 2:

2 + (0 / (√3/2))

Anything divided by 0 is undefined:

2 + undefined

Since the expression is undefined, we cannot determine a numerical value for it when x = π/6.