Question : If $\sec x+\cos x=2$, then the value of $\sec^{16} x+\cos^{16} x$ will be:
Option 1: $\sqrt3$
Option 2: $2$
Option 3: $1$
Option 4: $0$
Correct Answer: $2$
Solution :
Given: $\sec x+\cos x=2$
We know the algebraic identity, $(a-b)^2=a^2+b^2-2ab$.
$\frac{1}{\cos x}+\cos x=2$
Or, $\frac{1+\cos^2 x}{\cos x}=2$
Or, $\cos^2 x–2\cos x+1=0$
Or, $(\cos x-1)^2=0$
$\therefore \cos x=1$
So, $\sec x=1$.
The value of $\sec^{16} x+\cos^{16} x$ = $1+1=2$
Hence, the correct answer is $2$.
Related Questions
Know More about
Staff Selection Commission Sub Inspector ...
Result | Eligibility | Application | Selection Process | Cutoff | Admit Card | Preparation Tips
Get Updates Brochure
Your Staff Selection Commission Sub Inspector Exam brochure has been successfully mailed to your registered email id “”.
