Question

If 2 cos x + sin x = 1, then value of 7 cos x + 6 sin x can be

• A. 2
• B. 6
• C. 3
• D. 1

Answer 1

Answer: (A), (B)

The correct options are
A 2
B 6

If 2 cos x + sin x = 1, then value ………
2 cos x = 1 – sin x
On squaring $4co{s}^{2}x=1-2sinx+si{n}^{2}x$
$\Rightarrow 5si{n}^{2}x-2sinx-3=0\Rightarrow sinx=1,-\frac{3}{5}$
When sin x = 1, then cos x = 0 and so 7 cos x + 6 sin x = 6
When sin $x=-\frac{3}{5}$, then cos $x=\frac{4}{5}$
$\therefore$ cos x + 6 sin x = 2
Hence 7 cos x + 6 sin x = 6 or 2