not sure how to simplify tan(t+pi)/sin(t+2pi)
sin (t+2pi) = sin t
tan(t+pi) = tan t
tan t/sin t = (sin t/cos t)/sin t
= 1/cos t
= sec t
npgpp
To simplify the given expression tan(t+π)/sin(t+2π), we can use trigonometric identities and simplify step by step. Let's break down the process:
1. Start by applying the angle sum identity for tangent:
tan(t+π) = (tan(t) + tan(π)) / (1 - tan(t)tan(π))
Since tan(π) is undefined, we can simplify this to:
tan(t+π) = (tan(t) + 0) / (1 - 0)
tan(t+π) = tan(t) / 1 = tan(t)
2. Now we simplify the denominator sin(t+2π). Using the angle sum identity for sine:
sin(t+2π) = sin(t)cos(2π) + cos(t)sin(2π)
Since cos(2π) = 1 and sin(2π) = 0, the expression becomes:
sin(t+2π) = sin(t)⋅1 + cos(t)⋅0 = sin(t)
3. Finally, we substitute the simplified forms back into the original expression:
tan(t+π) / sin(t+2π) = tan(t) / sin(t)
The simplified expression is tan(t)/sin(t).
Remember, when simplifying trigonometric expressions, always look for identities and formulas that allow you to substitute and simplify step by step.