Simplifying the Expression sec(u) + c using Trigonometric Identities

secu+c

To simplify the expression sec(u) + c, we need to use the trigonometric identity that relates secant to cosine:

sec(u) = 1/cos(u)

Let’s substitute this in the expression:

sec(u) + c = 1/cos(u) + c

To combine these two terms, we need a common denominator

To simplify the expression sec(u) + c, we need to use the trigonometric identity that relates secant to cosine:

sec(u) = 1/cos(u)

Let’s substitute this in the expression:

sec(u) + c = 1/cos(u) + c

To combine these two terms, we need a common denominator. In this case, the least common denominator is cos(u).

Multiply the first fraction by cos(u)/cos(u):

1/cos(u) + c = (1*cos(u))/(cos(u)*cos(u)) + c = cos(u)/(cos(u)^2) + c

Now, we can simplify further. The expression cos(u)^2 is equal to 1, according to the Pythagorean identity:

cos(u)^2 + sin(u)^2 = 1

Therefore, cos(u)^2 = 1 – sin(u)^2

Substituting back into the expression:

cos(u)/(cos(u)^2) + c = cos(u)/(1 – sin(u)^2) + c

And there you have it, the simplified form of the expression sec(u) + c is cos(u)/(1 – sin(u)^2) + c.

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