Cosx/4*sin пи/5-sin x/4 * cos пи/5=-корень 2/2

Question

Cosx/4*sin пи/5-sin x/4 * cos пи/5=-корень 2/2

Answer 1

Sinπ/5*cosx/4-cosπ/5*sinx/4=sin(π/5-x/4)=cos(x/4+3π/10)
cos(x/4+3π/10)=-√2/2
x/4+3π/10=-3π/4+2πn U x/4+3π/10=3π/4+2πn
x/4=-21π/20+2πn U x/4=9π/20+2πn
x=-21π/5+8πn,n∈z U x=9π/5+8πn,n∈z

Answer 2

Cosx/4*Sin π/5 - Sin x/4 * Cos π/5=- √2/2
-( -Cosx/4*Sin π/5 + Sin x/4 * Cos π/5) = -√2/2
-Sin(x/4 - π/5) = -√2/2
Sin(x/4 - π/5) = √2/2
x/4 - π/5 = (-1)ⁿπ/4 + nπ, n ∈ Z
x/4 = π/5 +  (-1)ⁿπ/4 + nπ, n ∈ Z
x = 4π/5 + (-1)ⁿπ + 4nπ, n ∈ Z

Comments

спасибо большое, очень помогли, а sin^27-cos^27= корень 3/2

---

поможете?)))