Write the trigonometric expression in terms of sine and cosine, and then simplify.
tan u sin u + cos u
_____________.
sin*sin/cos + cos
common denominator cos
sin^2 + cos^2 all over common denominator. then
1/cos answer
When you say "then 1/cos answer" are you saying 1/cos is the answer or is it just adjacent to the rest
I'm confused
(sin^2 + cos^2)/cos = 1/cos
To simplify the trigonometric expression, we can rewrite the tangent (tan) in terms of sine (sin) and cosine (cos).
Recall that the tangent of an angle u is defined as the ratio of the sine of u to the cosine of u:
tan u = sin u / cos u
Using this definition, we can rewrite the expression as:
(sin u / cos u) * sin u + cos u
Next, we'll simplify the expression by combining like terms:
(sin^2 u / cos u) + cos u
Now, to combine the terms, we'll find a common denominator:
(sin^2 u + cos^2 u) / cos u
The numerator, sin^2 u + cos^2 u, is equal to 1 (as defined by the Pythagorean Identity). Therefore, the simplified expression is:
1 / cos u
In trigonometric terms, this can be written as:
sec u
So, the simplified expression of the given expression tan u sin u + cos u is sec u.