Which of the following statement is(are) true or false:
(i) $\tan^{-1}(1)=\frac{π}{4}$
(ii) $\sin^{-1}\frac{π}{2}$ not defined
(iii) $\tan^{-1}x=\cot^{-1}\frac{1}{x}$
(iv) $cosec^{-1}x=\sin^{-1}\frac{1}{x},|x|≥1$
Answer & explanation
Correct answer: option 3
(i) $\tan^{-1}(1)=\frac{π}{4}$ is true
(ii) $\sin^{-1}(1.57)$ = not defined ($\sin^{-1}x$ defined when -1 ≤ x ≤ 1) ⇒ The given equation is true
(iii) $\tan^{-1}x=\cot^{-1}\frac{1}{x}$ not true for all x
(iv) Standard result