Question

Cos50°/sin25°+cos25°

Answer 1

Ответ:

$\dfrac{cos50^\circ }{sin25^\circ +cos25^\circ }=\dfrac{cos^225^\circ -sin^225^\citc }{sin25^\circ +cos25^\circ }=\dfrac{(sin25^\circ -cos25^\circ )(sin25^\circ +cos25^\circ )}{sin25^\circ +cos25^\circ }=\\\\\\=sin25^\circ -cos25^\circ =sin25^\circ -cos(90^\circ -65^\circ )=sin25^\circ -sin65^\circ =\\\\\\=2\, sin\dfrac{25^\circ -65^\circ }{2}\cdot cos\dfrac{25^\circ +65^\circ }{2}=-2\, sin20^\circ \cdot cos45^\circ =-\sqrt2\, sin20^\circ$

Answer 2

Ответ:

Отв: ~2,42727

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Answer 3

To simplify the expression $\frac{\cos(50^\circ)}{\sin(25^\circ) + \cos(25^\circ)}$, you can use trigonometric identities.

1. Recall the trigonometric identity $\cos(2\theta) = 2\cos^2(\theta) - 1$.

2. You can rewrite $\cos(50^\circ)$ as $\cos(2 \cdot 25^\circ)$.

3. Using the identity, we have:

$\cos(2\cdot 25^\circ) = 2\cos^2(25^\circ) - 1$.

4. Now, rewrite the expression with the trigonometric identity:

$\frac{2\cos^2(25^\circ) - 1}{\sin(25^\circ) + \cos(25^\circ)}$.

Now, you have the expression simplified as much as possible.