How to simplify secx(sinx/tanx)?
secx(sinx/tanx)
= (1/cosx)(sinx)(cosx/sinx)
= 1
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To simplify the expression sec(x) * (sin(x) / tan(x)), we can use the trigonometric identities and simplify step by step:
Step 1: Recall the definitions of sec(x), sin(x), and tan(x):
sec(x) = 1 / cos(x)
sin(x) = sin(x)
tan(x) = sin(x) / cos(x)
Step 2: Substitute the definitions of sin(x) and tan(x) into the expression:
sec(x) * (sin(x) / tan(x)) = sec(x) * (sin(x) / (sin(x) / cos(x)))
Step 3: Simplify the expression by canceling out common terms:
sec(x) * (sin(x) / (sin(x) / cos(x))) = sec(x) * (1 / (1 / cos(x)))
= sec(x) * cos(x) / 1
= sec(x) * cos(x)
Step 4: Simplify further using the identity sec(x) * cos(x) = 1:
sec(x) * cos(x) = 1
Therefore, the simplified expression is 1.
To simplify the expression sec(x)(sin(x)/tan(x)), we can use trigonometric identities.
Let's start by simplifying the numerator sin(x)/tan(x):
Recall that tan(x) = sin(x)/cos(x). Therefore, sin(x)/tan(x) can be written as sin(x)*(cos(x)/sin(x)), which simplifies to just cos(x).
Now, our expression is sec(x)(cos(x)).
Again, let's apply a trigonometric identity. We know that sec(x) = 1/cos(x). Substitute this into our expression:
sec(x)(cos(x)) becomes (1/cos(x))(cos(x)).
Cos(x) in the numerator and denominator cancel out, resulting in a simplified expression of just 1.
Therefore, the simplified expression of sec(x)(sin(x)/tan(x)) is 1.