Question

Total number of solution of $16^{{\cos }^{2}x}+16^{{\sin }^{2}x}=10$ in $x\in [0,3\pi ]$ is equal to-

• A. 4
• B. 8
• C. 12
• D. 16

Answer 1

Answer: (C)

$16^{{\cos }^{2}x}+16^{1-{\cos }^{2}x}=10$
Let $16^{{\cos }^{2}x}=y,y+\frac{16}{y}=10,y^2-10y+16=0$
$\Rightarrow y=2,8\Rightarrow 16^{{\cos }^{2}x}=2,8\Rightarrow {\cos }^{2}x=\frac{1}{4},\frac{3}{4}$