Question

cot[cos^–1(3/4) + sin^–1(3/4) – sec^–13] =_________

(a) √2

(b) √3

(c) 2√3

(d) 2√2

Answer 1

The correct option (d) 2√2   

Explanation:

 sin^–1(3/4) + cos^–1(3/4) = (π/2)

given: cot[(π/2) – sec^–13] = tan(sec^–13) = tan[cos^–1(1/3)] 

∵ cos^–1x = tan^–1[√(1 – x²)/x]

∴ expression = tan ∙ tan^–1[√{1 – (1/9)}/(1/3)] 

= √8 = 2√2.