Tanx + sinxsecx/ cscxtanx
if you want to simplify
(tanx + sinx secx)/(cscx tanx)
then you have
(tanx + tanx)/secx
2tanx * cosx
2sinx
To simplify the expression tan(x) + sin(x)sec(x)/csc(x)tan(x), we'll start by simplifying each term individually.
First, let's simplify sin(x)sec(x) / csc(x)tan(x).
Using trigonometric identities:
sin(x)sec(x) / csc(x)tan(x) = sin(x) * (1/cos(x)) / (1/sin(x)) * tan(x)
Next, simplify each term:
sin(x) * (1/cos(x)) = sin(x)/cos(x) = tan(x)
(1/sin(x)) * tan(x) = tan(x)/sin(x) = sec(x)
So, sin(x)sec(x) / csc(x)tan(x) simplifies to tan(x) / sec(x).
Now, substitute this simplified expression back into the original equation:
tan(x) + tan(x) / sec(x)
To add these two terms, we need to find a common denominator. Recall that sec(x) = 1/cos(x).
The common denominator for tan(x) and 1/cos(x) is cos(x).
tan(x) + tan(x) / sec(x) = tan(x) + tan(x) / (1/cos(x))
Now, let's convert tan(x) / (1/cos(x)) into a single fraction:
tan(x) + cos(x) * tan(x) / 1
Combine the terms:
tan(x) + cos(x) * tan(x) = tan(x) * (1 + cos(x))
Therefore, the simplified expression of tan(x) + sin(x)sec(x) / csc(x)tan(x) is tan(x) * (1 + cos(x)).