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Question

Find the value of each of the following:

(i)tan-113(ii)tan-1-13(iii)tan-1cosπ2(iv)tan-12cos2π3


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Solution

Solve for the required values

(i) tan-113

Let tan-113=θ

θ=tan-113=tan-1tanπ6θ=π6

(ii) tan-1-13

Let tan-1-13=θ

θ=tan-1-13=tan-1tan-π6θ=-π6

(iii) tan-1cosπ2

Let tan-1cosπ2=θ

θ=tan-1cosπ2=tan-10θ=0

(iv) tan-12cos2π3

Let tan-12cos2π3=θ

θ=tan-12cos2π3=tan-12cosπ-π3=tan-1-2cosπ3=tan-1-2×12=tan-1-1θ=-π4


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