A) \[{{\tan }^{-1}}(2\sqrt{2})\]
B) \[{{\tan }^{-1}}(3\sqrt{2})\]
C) \[{{\tan }^{-1}}(3\sqrt{3})\]
D) \[{{\tan }^{-1}}(5\sqrt{2})\]
Correct Answer: A
Solution :
If \[\sin x=\cos x\Rightarrow x=\pi /4\] If \[y=\sin x\Rightarrow {{\left( \frac{dy}{dx} \right)}_{x=\pi /4}}=\frac{1}{\sqrt{2}}\] If \[y=\cos x\Rightarrow {{\left( \frac{dy}{dx} \right)}_{x=\pi /4}}=\frac{-1}{\sqrt{2}}\] \[\tan \theta =\frac{{{m}_{1}}-{{m}_{2}}}{1+{{m}_{1}}{{m}_{2}}}=2\sqrt{2}\Rightarrow \,\theta ={{\tan }^{-1}}(2\sqrt{2})\].
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