prove the identity:
cos(x)*csc(x)*tan(x)=1
To prove the given identity, we need to manipulate the left-hand side of the equation (LHS) until it equals the right-hand side (RHS), which in this case is 1.
Given: cos(x) * csc(x) * tan(x)
First, let's rewrite csc(x) and tan(x) in terms of sine and cosine:
csc(x) = 1/sin(x)
tan(x) = sin(x)/cos(x)
Substituting these values, the LHS becomes:
cos(x) * (1/sin(x)) * (sin(x)/cos(x))
Now, cancel out the common terms in the numerator and denominator:
cos(x) * (1/cos(x))
Since cos(x)/cos(x) is equal to 1, the expression simplifies to:
1
Therefore, we have proven that cos(x) * csc(x) * tan(x) is equal to 1, as desired.