Question

The general solution of the equation $\cos x+\sec x=2$ is given by-

• A. $2n\pi ;n\in I$
• B. $n\pi ;n\in I$
• C. $\frac{n\pi }{4};n\in I$
• D. $\frac{n\pi }{2};n\in I$

Answer 1

The correct option is A $2n\pi ;n\in I$

Simplifying $\cos x+\sec x=2$.

$\cos x+\frac{1}{\cos x}=2$

${\cos }^{2}x+1=2\cos x$

${\cos }^{2}x-2\cos x+1=0$

${\left(\cos x-1\right)}^2=0$

$\cos x-1=0$

$\cos x=1$

$\cos x=\cos 0^{\circ }$

$x=2n\pi$