simplify: tanx/secx+1
Identities:
tan x = sin x / cos x
sec x = 1 / cos x
If your problem is this:
(tanx/secx) + 1
Then:
[(sin x / cos x) / (1 / cos x)] + 1 = sin x + 1
If your problem is this:
tan x / (sec x + 1)
Then: (sin x / cos x ) / [(1 / cos x) + 1] = (sin x / cos x) / [(1 / cos x) + (cos x / cos x)] = (sin x / cos x) / [(1 + cos x)/cos x] = sin x / (1 + cos x)
I hope this helps.
Why did the triangle go to the party? Because it wanted to tangent and secant with all the other angles! Simplifying the expression tan(x)/sec(x) + 1, we can rewrite sec(x) as 1/cos(x). Now we have tan(x)/(1/cos(x)) + 1. Multiplying by the reciprocal, this becomes tan(x) * cos(x)/1 + 1. Simplifying further, we get (sin(x)/cos(x)) * cos(x) + 1, which simplifies to sin(x) + 1. So, the simplified expression is sin(x) + 1.
To simplify the expression tan(x) / sec(x) + 1, we can rewrite tan(x) and sec(x) in terms of sine (sin) and cosine (cos) functions.
Recall that tan(x) = sin(x) / cos(x) and sec(x) = 1 / cos(x).
Substituting these values into the expression, we get:
(sin(x) / cos(x)) / (1 / cos(x)) + 1
Next, we can simplify this expression by multiplying the numerator and denominator of the first fraction by cos(x):
(sin(x) / cos(x)) * (cos(x) / 1) + 1
Simplifying further, we have:
sin(x) + 1
Therefore, the simplified expression is sin(x) + 1.
To simplify the expression tanx/secx+1, we can start by simplifying the individual trigonometric functions in the expression.
The reciprocal of secx is 1/cosx. So the expression can be rewritten as tanx/(1/cosx) + 1.
Now, we have a fraction divided by another fraction. To simplify this, we can multiply the numerator by the reciprocal of the denominator.
Therefore, tanx/(1/cosx) + 1 can be rewritten as tanx * (cosx/1) + 1.
Simplifying further, we have tanx * cosx + 1.
So the simplified expression is tanx * cosx + 1.