Question

The general solution of the equation ${\log }_5\tan \theta ={\log }_{5}4.{\log }_4\left(3\sin \theta \right)$ is-

• A. $n\pi$
• B. $2n\pi +{\cos }^{-1}\left(1/3\right)$
• C. $2n\pi -{\cos }^{-1}\left(1/3\right)$
• D. All are correct

Answer 1

The correct option is A $n\pi$

We have to find the general solution of the equation ${\log }_5\tan \theta ={\log }_{5}4.{\log }_4\left(3\sin \theta \right)$

Now

${\log }_5\tan \theta$ $={\log }_{5}4.{\log }_4\left(3\sin \theta \right)$

$\Rightarrow \tan \theta =4\log 4\left(\sin \right)$

$\Rightarrow \theta =n\pi n\in I$

Hence, the option $\left(A\right)$ is correct.