The principal value of (1) +(-12) is:

The given function is (1) +(-12) . Let us look at the first term of the given function. The first term is (1) . We know that tan π4 = 1. Therefore, we have (1) =π4 . The range of the inverse tangent function is (-π2,π2). Since π4 ∈ (−π2,π2), it is the principal value of is (1) .Next, let us look at the second term of the given function. The second term is -12) . We know that cos2π3=−-12. Hence, we have -12) =2π3 . Now, we are aware that the range of the inverse cosine function is [0, π]. We can see that 2π3 ∈ [0, π].Therefore, -12) =2π3 is its principal value.So, the principal value of the given function is the following, (1) +(-12) = π4+2π3⇒ (1) +(-12) = 3π+8π12∴ (1) +(-12) = 11π12Hence, the principal value of the given function is 11π12

The principal value of (1) +(-12) is:

The given function is (1) +(-12) . Let us look at the first term of the given function. The first term is (1) . We know that tan π4 = 1. Therefore, we have (1) =π4 . The range of the inverse tangent function is (-π2,π2). Since π4 ∈ (−π2,π2), it is the principal value of is (1) .Next, let us look at the second term of the given function. The second term is -12) . We know that cos2π3=−-12. Hence, we have -12) =2π3 . Now, we are aware that the range of the inverse cosine function is [0, π]. We can see that 2π3 ∈ [0, π].Therefore, -12) =2π3 is its principal value.So, the principal value of the given function is the following, (1) +(-12) = π4+2π3⇒ (1) +(-12) = 3π+8π12∴ (1) +(-12) = 11π12Hence, the principal value of the given function is 11π12