Rewrite the expression secvcscv+cotv/secvcscv in terms of sine and cosine, then simplify using trigonometric identities.
well, you know that
secv = 1/cosv
cscv = 1/sinv
cotv = cosv/sinv
so give it your best shot. Surely you recall your Algebra I
come back with some work indicating how far you get.
To rewrite the expression secvcscv+cotv/secvcscv in terms of sine and cosine, we can start by recalling the definitions of the trigonometric functions:
sec(v) = 1/cos(v)
csc(v) = 1/sin(v)
cot(v) = cos(v)/sin(v)
By substituting these definitions, we can rewrite the expression as:
(1/cos(v))(1/sin(v)) + (cos(v)/sin(v)) / ((1/cos(v))(1/sin(v)))
Now, let's simplify the expression using trigonometric identities.
First, we can simplify the numerator of the first term:
(1/cos(v))(1/sin(v)) = 1/(cos(v)sin(v))
Next, let's simplify the denominator of the second term:
(1/cos(v))(1/sin(v)) = 1/(cos(v)sin(v))
Now, let's simplify the expression further:
1/(cos(v)sin(v)) + (cos(v)/sin(v)) / (1/(cos(v)sin(v)))
To simplify this expression, we need to combine the terms and get a common denominator.
The common denominator is (cos(v)sin(v)):
= (1 + cos(v))/sin(v)
Thus, the simplified expression in terms of sine and cosine is:
(1 + cos(v))/sin(v)