Prove this identity. State any restrictions on the variables.
sin x/(tan x)= cos x
To prove the identity sin x / tan x = cos x, we first need to simplify both sides of the equation.
Starting with the left-hand side:
sin x / tan x
Using the definition of tangent, we can rewrite tan x as sin x / cos x:
sin x / (sin x / cos x)
Now, we can simplify the expression by multiplying the numerator by the reciprocal of the denominator:
(sin x) * (cos x / sin x)
The sin x in the numerator cancels out with the sin x in the denominator, leaving us with:
cos x
This is the same as the right-hand side of the equation, cos x.
Therefore, we have proven that sin x / tan x = cos x.
As for the restrictions on the variables, we need to consider the values of x that would result in division by zero. In this case, we need to ensure that the value of x does not make the denominator, tan x, equal to zero. The tangent function is undefined for x values that are odd multiples of π/2 (π/2, 3π/2, 5π/2, etc.). Therefore, the restriction on the variable x is that x cannot be equal to π/2 plus or minus any odd multiple of π/2.
tanx=?
http://www.mathwords.com/t/trig_identities.htm
also, what value(s) would be unacceptable in the denominator?