Answer:
[tex]sin(u) cot(u) cos(u) = cos^{2}(u)[/tex]
Step-by-step explanation:
[tex]sin(u) cot(u) cos(u)[/tex]
First, let us simplify cot(u) as follows:
cot (u) = [tex]\frac{1}{tan(u)}[/tex]
also, [tex]tan (u) = \frac{sin (u)}{cos(u)}[/tex]
∴ [tex]\frac{1}{tan(u)} = \frac{1}{\frac{sin(u)}{cos(u)} } = \frac{cos(u)}{sin(u)}[/tex]
Hence the original expression becomes:
[tex]sin(u).\frac{cos(u)}{sin(u)} .cos(u)[/tex]
Next, sin(u) will cancel each other out, leaving the expression below:
[tex]cos(u) . cos(u) = cos^{2} (u)[/tex]
hence:
[tex]sin(u) cot(u) cos(u) = cos^{2}(u)[/tex]
I also found a similar expression with a plus (+) sign after the "sin(u)" online, and if this was your question, the solution will be as follows:
sin(u)+ cot(u) cos(u)
[tex]sin(u) + \frac{cos(u)}{sin(u)} . cos (u)[/tex]
[tex]= sin(u) + \frac{cos^{2} (u)}{sin(u)}[/tex]
[tex]sin(u).\frac{sin(u)}{sin(u)} + \frac{cos^{2}(u) }{sin(u)} \\[/tex] (note that [tex]\frac{sin(u)}{sin(u)} = 1[/tex], hence multiplying it with sin(u) does not change anything in the expression.)
[tex]\frac{sin^{2} (u)}{sin(u)} + \frac{cos^{2}(u) }{sin(u)} = \frac{sin^{2}(u) + cos^{2}(u) }{sin(u)}[/tex]
Now the relationship sin²(u) + cos²(u) = 1
Therefore:
[tex]\frac{sin^{2}(u) + cos^{2}(u) }{sin(u)} = \frac{1}{sin(u)}[/tex]
Hence, [tex]sin(u)+ cot(u) cos(u) = \frac{1}{sin(u)}[/tex]
