"What does cos⁡xsin⁡x equal?" solved and explained

High School
Geometry
Trigonometry
Trigonometric Functions

Judith McQueen

Answered question

2021-12-26

What does

\cos x \sin x

equal?

Answer & Explanation

Serita Dewitt

Beginner2021-12-27Added 41 answers

Explanation:
So we have

\cos (x) \sin (x)

If we multiply it by two we have

2 \cos (x) \sin (x)

Which we can say its

Corgnatiui

Beginner2021-12-28Added 35 answers

$\sin (A + B) = \sin (A) \cos (B) + \cos (A) \sin (B)$
Now let A = B = x. So we get:
$\sin (x + x) = \sin (2 x) = \sin (x) \cos (x) + \cos (x) \sin (x) = 2 \sin (x) \cos (x)$
Therefore,
$\sin (x) \cos (x) = (1 / 2) \sin (2 x)$
Hope this helps!

Vasquez

Expert2022-01-08Added 669 answers

Look into the following:
$\begin{matrix} \sin (x + y) = \sin (x) \cos (y) + \cos (x) \sin (y) \\ N o w s e t x = y, \\ N o w, \\ \sin (x + x) = \sin (x) \cos (x) + \cos (x) \sin (x) \\ \Rightarrow \sin (2 x) = 2 \sin (x) \cos (x) \\ \Rightarrow \sin (x) \cos (x) = \frac{1}{2} \sin (2 x) \end{matrix}$

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