What does \cos x \sin x equal?

Judith McQueen 2021-12-26 Answered
What does \(\displaystyle{\cos{{x}}}{\sin{{x}}}\) equal?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Serita Dewitt
Answered 2021-12-27 Author has 5497 answers
Explanation:
So we have
\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}\)
If we multiply it by two we have
\(\displaystyle{2}{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}\)
Which we can say it's a sum
\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}+{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}\)
Which is the double angle formula of the sine
\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}+{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}={\sin{{\left({2}{x}\right)}}}\)
But since we multiplied by 2 early on to get to that, we need to divide by two to make the equality, so
\(\displaystyle{\cos{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}={\frac{{{\sin{{\left({2}{x}\right)}}}}}{{{2}}}}\)
Not exactly what you’re looking for?
Ask My Question
0
 
Corgnatiui
Answered 2021-12-28 Author has 831 answers

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

0
Vasquez
Answered 2022-01-08 Author has 9055 answers

Look into the following:
\(\begin{array}{}\sin(x+y)=\sin(x)\cos(y)+\cos(x)\sin(y) \\Now\ set\ x=y, \\Now, \\\sin(x+x)=\sin(x)\cos(x)+\cos(x)\sin(x) \\\Rightarrow \sin(2x)=2\sin(x)\cos(x) \\\Rightarrow \sin(x)\cos(x)=\frac{1}{2}\sin(2x) \end{array}\)

0

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...