(i) sin(tan^-1(1)) is equal to (a) 1/√2 (b) 1 (c) 1/2 (d) √3/2

Question

(i) sin(tan^-1(1)) is equal to

(a) \(\frac{1}{\sqrt{2}}\)

(b) 1

(c) \(\frac{1}{2}\)

(d) \(\frac{\sqrt{3}}{2}\)

(ii) If x ∈ (0, \(\frac{π}{2}\)) , show that

cot^-1(\(\frac{\sqrt{1+sinx}+ \sqrt{1-sinx}}{\sqrt{1+sinx}+{\sqrt{1-sinx}}}\)) = \(\frac{x}{2}\)

Answer 1

(i) (a) \(\frac{1}{\sqrt{2}}\)

(ii)