To solve the expression 1 + tan²(a) + 1 + cot²(a) + 1 + tan(a) + 1 + cot²(a) + tan²(a), we can first simplify it step by step.
First, let’s rewrite the components of the expression:
- tan²(a) = sin²(a)/cos²(a)
- cot²(a) = cos²(a)/sin²(a)
Now let’s organize the expression:
- We have 1 + 1 + 1 + 1 + 1 = 5 (the constant terms).
- Then, we combine the tan²(a) and cot²(a).
Now let’s combine the tangents:
The expression simplifies to:
5 + 2tan²(a) + 2cot²(a) + tan(a) + cot(a)
Next, using the Pythagorean identities, we recall that:
tan²(a) + cot²(a) = tan²(a) + 1/tan²(a) = (tan²(a) + 1)^2 - 2
This implies that if you compute tan²(a) + cot²(a), you’ll notice it can be expressed in terms of constants.
Add everything together appropriately while considering possible simplifications from identities. However, the expansions might keep leading to summed derivatives based on a chosen angle.
This concludes a simplified approach to finding the value of the original equation.