Question

If ${\cos }^2\alpha =a+3$,

solution of equation ${\cos }^{2}x={\cos }^2\alpha$ is

• A. $2n\pi \pm \left(\sqrt{a+3}\right)$
• B. $n\pi \pm {\cos }^{-1}\left(\sqrt{a+3}\right)$
• C. $n\pi +(-1{)}^n{\cos }^{-1}(\sqrt{a+3})$
• D. None of these

Answer 1

Answer: (B)

$n\pi \pm {\cos }^{-1}\left(\sqrt{a+3}\right)$

We know that,

${\cos }^{2}x=a+3={\cos }^2\alpha where,\alpha ={\cos }^{-1}\sqrt{a+3}So,{\cos }^{2}x={\cos }^2\alpha \Rightarrow x=n\pi \pm \alpha ,nϵZ\Rightarrow x=n\pi \pm {\cos }^{-1}\sqrt{a+3}$