verify the identity.
cotx secx sinx=1
Write cot and sec in terms of sin and cos, multiply it all together and watch everything cancel.
In case you forgot:
cot = cos/sin
sec = 1/cos
To verify the identity cot(x) sec(x) sin(x) = 1, we need to simplify the left-hand side (LHS) of the equation and show that it is equal to 1.
Let's start by applying the reciprocal identities:
cot(x) = cos(x) / sin(x) --> (1)
sec(x) = 1 / cos(x) --> (2)
Now, substitute equations (1) and (2) into the LHS of the equation:
LHS = cot(x) sec(x) sin(x)
= (cos(x) / sin(x)) * (1 / cos(x)) * sin(x)
= cos(x) * (1 / cos(x)) * sin(x) / sin(x)
= (cos(x) * sin(x)) / (cos(x) * sin(x))
Using the cancelation property of multiplication/division, we can cancel out the common terms:
LHS = 1
Therefore, the LHS of the equation simplifies to 1, which implies that the given identity is verified.
To verify the identity cot(x) sec(x) sin(x) = 1, we can manipulate the left-hand side of the equation and simplify it to see if it is equal to the right-hand side of the equation.
Let's start by expressing the trigonometric functions cot(x), sec(x), and sin(x) in terms of sine and cosine functions:
cot(x) = cos(x) / sin(x)
sec(x) = 1 / cos(x)
Substituting these expressions into the original equation:
cot(x) sec(x) sin(x) = (cos(x) / sin(x)) * (1 / cos(x)) * sin(x)
Simplifying the expression:
cot(x) sec(x) sin(x) = (cos(x) * 1 * sin(x)) / (sin(x) * cos(x))
= cos(x) * sin(x) / sin(x) * cos(x)
Now, we can cancel out sin(x) and cos(x):
cot(x) sec(x) sin(x) = 1
Therefore, we have verified that cot(x) sec(x) sin(x) = 1.