Evaluate each of the following: (i) sin (sin^-1 7/25) (ii) sin (cos^-1 5/13)

Question

Evaluate: 

(i) sin (sin^-1 \({\frac{7}{25}}\))

(ii) sin (cos^-1\({\frac{5}{13}}\))

Answer 1

(i) Given as sin(sin^-1 7/25)

Let y = sin^-1 7/25

sin y = 7/25 where y ∈ [0, π/2]

On, substituting these values in sin (sin^-1 7/25), we get

sin (sin^-1 7/25) = 7/25

(ii) Given as sin (cos^-1 5/13)

By substituting cos y value, we get