Question

$ta{n}^{-1}\left[cos\left(2ta{n}^{-1}\frac{3}{4}\right)+sin\left(2co{t}^{-1}\frac{1}{2}\right)\right]$ is

• A. not defined
• B. $\frac{\pi }{4}$
• C. $>\frac{\pi }{4}$
• D. $<\frac{\pi }{4}$

Answer 1

Answer: (C)

$cos\left(2ta{n}^{-1}\frac{3}{4}\right)=\frac{1-\frac{9}{16}}{1+\frac{9}{16}}=\frac{7}{25}$
$sin\left(2co{t}^{-1}\frac{1}{2}\right)=sin\left(2ta{n}^{-1}2\right)$
$=\frac{2\times 2}{1+4}=\frac{4}{5}$
$ta{n}^{-1}\left(\frac{7}{25}+\frac{4}{5}\right)$
$=ta{n}^{-1}\frac{27}{25}>\frac{\pi }{4}$