Question

Sin a + cos a =4/9 sin a * cos a = ?

Answer 1

Ответ: Решение на фото

Пошаговое объяснение:

1) Возводим обе части данного равенства в квадрат.

2) Раскрываем квадрат, используя формулу квадрат суммы.

3) Используем основное тригонометрическое тождество.

4)-6) Находим произведение синуса на косинус.

Answer 2

To find the value of sin(a) * cos(a), we can use some trigonometric identities. Let's start by squaring the equation sin(a) + cos(a) = 4/9:

(sin(a) + cos(a))^2 = (4/9)^2

Expanding the left-hand side:

sin^2(a) + 2sin(a)cos(a) + cos^2(a) = 16/81

Now, we can use the trigonometric identity sin^2(a) + cos^2(a) = 1:

1 + 2sin(a)cos(a) = 16/81

Now, rearrange the equation to solve for sin(a) * cos(a):

2sin(a)cos(a) = 16/81 - 1

2sin(a)cos(a) = 16/81 - 81/81

2sin(a)cos(a) = (16 - 81)/81

2sin(a)cos(a) = -65/81

Now, divide both sides by 2:

sin(a) * cos(a) = -65/162

So, the value of sin(a) * cos(a) is -65/162.