If 2 cos x +sin x =1 then 7 cos x + 6 sin x=___

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Solution

The correct options are
A
6

B
2

I = 7 cos x +6 sin x
= 6 (2 cos x + sin x)-5 cos x.
= 6-5 cos x.
Now, 2 cos x +sin x =1
$\Rightarrow s i n x = 1 - 2 c o s x \Rightarrow s i n^{2} x = 1 + 4 c o s^{2} x - 4 c o s x . \Rightarrow 1 - s i n^{2} x + 4 c o s^{2} x - 4 c o s x = 0 \Rightarrow 5 c o s^{2} x - 4 c o s x = 0$
$\Rightarrow c o s x = 0$ or $\frac{4}{5}$
$∴ I = 6 o r 2$

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