Find the value of tan-1 (1) and tan-1 (tan 1).
To find the values of the above inverse trigonometric ratios, we will use trigonometric identities.
Answer: The value of tan-1 (1) is π / 4, and tan-1 (tan 1) is π / 4
Let's find the values of inverse trigonometric ratios.
(i) Let tan-1 (1) = θ
⇒ tan θ = 1
Since we know that the range of principal value of tan is (-π / 2, π / 2)
Also we know that tan (π / 4) = 1
⇒ tan θ = tan (π / 4)
⇒ θ = π / 4
(ii) As we know that tan-1 (tan x) = x for x belongs to (- π / 2, π / 2)
⇒ tan-1 (tan 1) = 1