Question

Sin^3(п/4)+cos^3(п/4)-sin( п/4)=0

Answer 1

Используем значения синуса и косинуса в 45 градусах

Answer 2

Let's solve the equation step by step:

1. First, let's simplify the trigonometric terms using the identity: $\sin^3(\theta) = (\sin(\theta))^3$.

$\sin^3(\frac{\pi}{4}) + \cos^3(\frac{\pi}{4}) - \sin(\frac{\pi}{4}) = (\sin(\frac{\pi}{4}))^3 + (\cos(\frac{\pi}{4}))^3 - \sin(\frac{\pi}{4})$

2. Now, we can use the trigonometric values for $\frac{\pi}{4}$.

Recall that $\sin(\frac{\pi}{4}) = \cos(\frac{\pi}{4}) = \frac{\sqrt{2}}{2}$.

So, the equation becomes:

$(\frac{\sqrt{2}}{2})^3 + (\frac{\sqrt{2}}{2})^3 - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{8} + \frac{\sqrt{2}}{8} - \frac{\sqrt{2}}{2}$

3. Now, let's simplify the expression:

$\frac{\sqrt{2}}{8} + \frac{\sqrt{2}}{8} - \frac{\sqrt{2}}{2} = \frac{2\sqrt{2}}{8} - \frac{\sqrt{2}}{2} = \frac{\sqrt{2}}{4} - \frac{\sqrt{2}}{2} = \frac{-\sqrt{2}}{4}$

4. So, the final solution to the equation is:

$\sin^3(\frac{\pi}{4}) + \cos^3(\frac{\pi}{4}) - \sin(\frac{\pi}{4}) = \frac{-\sqrt{2}}{4}$