The value of \(\cot \left[\cos^{−1}\left(\frac{7}{25}\right)\right]\) is

Explanation:

If sinθ = x ⇒ θ = sin^-1x, for θ ∈ [-π/2, π/2]

cot (cot^-1 x) =x for x ∈ R

We have, \(\cot \left[\cos^{−1}\left(\frac{7}{25}\right)\right]\)

Let \(\cos^{−1}\left(\frac{7}{25}\right)\)= θ

⇒ cosθ = 7/25

⇒ sinθ = 24/25

⇒ cotθ = 7/24

∴  \(\cot \left[\cos^{−1}\left(\frac{7}{25}\right)\right]\)

= cotθ 

= 7/24