Question

The value of $\left(\sin \right(\log i^i){)}^3+(\cos \left(\log i^i\right){)}^3$ equals?

• A. 3
• B. 2
• C. 1
• D. None of these

Answer 1

The correct option is D None of these

Given ,${\left\{\sin \right(\log i^i\left)\right\}}^3+{\left(\cos \right(\log i^{-i}\left)\right)}^3$

$={\left\{\sin \right({\log }_e{e}^{-\pi /2}\left)\right\}}^3+{\left\{\cos \right({\log }_e{e}^{-\pi /2}\left)\right\}}^2(\because i^{-i}=e^{-\pi /2})$

$={\left\{\sin \right(\frac{-\pi }{2}{\log }_{e}e\left)\right\}}^3+{\left\{\cos \right(\frac{-\pi }{2}{\log }_{e}e\left)\right\}}^3$

$={\left\{sin\right(-\pi /2\left)\right\}}^3{\left\{\cos \right(-\pi /2\left)\right\}}^3(\because {\log }_{e}e=1)=-1$