Question

10cos105°/sin15°*cos60°

Answer 1

Условие можно прочитать по-разному

$1)~\boldsymbol{\dfrac{10\cos105\textdegree}{\sin15\textdegree}\cdot \cos60\textdegree=}\dfrac{10\cos(90\textdegree+15\textdegree)}{\sin15\textdegree}\cdot \dfrac 12=\\\\=-\dfrac{10\sin15\textdegree}{\sin15\textdegree}\cdot \dfrac 12=-10\cdot \dfrac 12\boldsymbol{=-5}$

$2)~\boldsymbol{\dfrac{10\cos105\textdegree}{\sin15\textdegree\cdot \cos60\textdegree}=}\dfrac{10\cos(90\textdegree+15\textdegree)}{\sin15\textdegree\cdot \frac 12}=\\\\=-\dfrac{10\sin15\textdegree}{\sin15\textdegree}\cdot \dfrac 21=-10\cdot 2\boldsymbol{=-20}$

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Использована формула приведения

$\cos (90\textdegree+\alpha)=-\sin \alpha$

Answer 2

To calculate the value of the expression 10cos(105°)/sin(15°) * cos(60°), let's break it down step by step.

First, let's evaluate the trigonometric functions individually:

cos(105°) ≈ 0.2588190451 (rounded to 10 decimal places) sin(15°) ≈ 0.2588190451 (rounded to 10 decimal places) cos(60°) = 0.5

Now, substitute these values into the expression:

10cos(105°)/sin(15°) * cos(60°) ≈ 10 * 0.2588190451 / 0.2588190451 * 0.5

Simplifying further:

≈ 10 * 1 / 1 * 0.5 ≈ 10 * 0.5 ≈ 5

Therefore, 10cos(105°)/sin(15°) * cos(60°) is approximately equal to 5.