sin²u + tan²u + cos²u/ sec u
simplify
To simplify the expression sin²u + tan²u + cos²u / sec u, we can use trigonometric identities.
1. Recall the Pythagorean identity for sine and cosine: sin²u + cos²u = 1. We can substitute this into our expression to simplify it.
(sin²u + tan²u) + cos²u / sec u
2. Next, recall the identity for tangent in terms of sine and cosine: tan u = sin u / cos u. We can substitute this into our expression as well.
(sin²u + sin²u / cos²u) + cos²u / sec u
3. Now, let's simplify the terms separately.
a. Simplifying the numerator of the first term: (sin²u + sin²u) = 2sin²u
b. Simplifying the denominator of the first term: / cos²u
c. Simplifying the second term: cos²u / sec u
Remember that sec u is the reciprocal of cos u, so sec u = 1 / cos u.
Substituting this into the second term: cos²u / (1 / cos u) = cos²u * cos u = cos³u
4. Finally, let's combine the simplified terms.
2sin²u / cos²u + cos³u
Now, the expression is simplified as 2sin²u / cos²u + cos³u.