Question

If $y={\sin }^{-1}2x+{\tan }^{-1}3x+{\cos }^{-1}2x+{\cot }^{-1}3x$ then

• A. $y^{\prime }\left(0\right)=0$
• B. $y_5=y_6$
• C. $y_2=y_4$
• D. None of these

Answer 1

Answer: (A), (B), (C)

The correct options are
A $y^{\prime }\left(0\right)=0$
B $y_5=y_6$
C $y_2=y_4$

Since ${\sin }^{-1}\theta +{\cos }^{-1}\theta =\frac{\pi }{2}$
and ${\tan }^{-1}\theta +{\cot }^{-1}\theta =\frac{\pi }{2}$
Hence $y=\pi$
$\Rightarrow y_n\left(x\right)=0$
for all $x$ and for all $n$