Tanø(secø+2)
To simplify the expression Tan(ø(sec(ø+2))), we can start by applying the trigonometric identity:
Tan(u) = Sin(u) / Cos(u)
Using this identity, we can rewrite the expression as:
Sin(ø(sec(ø+2))) / Cos(ø(sec(ø+2)))
Next, we need to simplify the expression inside the trigonometric functions.
Inside the Sin function:
sec(u) = 1 / Cos(u)
Therefore, sec(ø+2) = 1 / Cos(ø+2)
Inside the Cos function:
sec(u) = 1 / Cos(u)
Therefore, sec(ø+2) = 1 / Cos(ø+2)
Now we can rewrite the expression:
Sin(ø(1/Cos(ø+2))) / Cos(ø(1/Cos(ø+2)))
We still have a product inside the trigonometric functions. We can simplify this by using the identity:
Sin(u * v) = Sin(u) * Cos(v) + Cos(u) * Sin(v)
Applying this identity to the expression, we have:
Sin(ø) * Cos(1/Cos(ø+2)) + Cos(ø) * Sin(1/Cos(ø+2)) / Cos(ø) * Cos(1/Cos(ø+2))
The trigonometric functions inside the expression are not simplifiable any further. Therefore, the simplified expression is:
Sin(ø) * Cos(1/Cos(ø+2)) + Cos(ø) * Sin(1/Cos(ø+2)) / (Cos(ø) * Cos(1/Cos(ø+2)))