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Domain and Range of Trigonometric Ratios

If 2 cos x +s...

Question

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

A

6

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B

2

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C

1

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D

3

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Solution

The correct options are
A
6

B
2

I =y 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
$\Rightarrow s i n x = 1 - 2 c o s x . \Rightarrow s i n^{2} x = 1 + 4 c o s^{2} x - 4 c o s x . = 1 - c o s^{2} x \Rightarrow 5 c o s^{2} x - 4 c o s x = 0$
$\Rightarrow c o s^{2} x = 0$ or $\frac{4}{5}$
$∴ I = 6$ or 2.

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

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Domain and Range of Trigonometric Ratios

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