Question

Consider the following statements:
1. ${\tan }^{-1}1+{\tan }^{-1}\left(0.5\right)=\frac{\pi }{2}$
2. ${\sin }^{-1}\frac{1}{3}+{\cos }^{-1}\frac{1}{3}=\frac{\pi }{2}$
Which of the above statements is/are correct ?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is B 2 only

We know that

${\tan }^{-1}x+{\cot }^{-1}x=\frac{\pi }{2}$ for $x\in$R

and

${\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}$ for $x\in$(-1,1)

$\Rightarrow$ ${\tan }^{-1}1+{\tan }^{-1}\frac{1}{2}={\tan }^{-1}1+{\cot }^{-1}2\ne \frac{\pi }{2}$

and

${\sin }^{-1}\frac{1}{3}+{\cos }^{-1}\frac{1}{3}=\frac{\pi }{2}$

Hence, only second statement is correct.