Question

Sin(п/4+a)-cos(п/4-a)=0

Answer 1

Решение задания смотри на фотографии

Answer 2

Let's solve the trigonometric equation:

sin(π/4 + a) - cos(π/4 - a) = 0

To solve this equation, we can use the trigonometric identities:

1. sin(α + β) = sin(α) * cos(β) + cos(α) * sin(β)
2. cos(α - β) = cos(α) * cos(β) + sin(α) * sin(β)

Let's apply these identities to the equation:

sin(π/4 + a) - cos(π/4 - a) = sin(π/4) * cos(a) + cos(π/4) * sin(a) - cos(π/4) * cos(a) + sin(π/4) * sin(a) = 0

Now, simplify the equation:

(√2/2) * cos(a) + (√2/2) * sin(a) - (√2/2) * cos(a) + (√2/2) * sin(a) = 0

Combine like terms:

(√2/2 - √2/2) * cos(a) + (√2/2 + √2/2) * sin(a) = 0

0 * cos(a) + (√2 * sin(a)) = 0

Now, we have:

√2 * sin(a) = 0

To find the solutions for 'a', we need to set sin(a) = 0 and solve for 'a'.

sin(a) = 0

The values of 'a' that satisfy the equation sin(a) = 0 are multiples of π (pi). In other words:

a = n * π, where n is an integer.

So, the solutions for 'a' are a = 0, a = π, a = 2π, a = -π, a = -2π, and so on.