Question

If 2 cos theta +sin theta=1 then the value of 7costheta+ 6sintheta can be equal to

Answer 1

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Answer 2

Answer is $\frac {13}{3}$

Step-by-step explanation:

$2cos\Theta + sin\Theta = 1$

$cos\Theta + cos\Theta + sin\Theta = 1$

$cos\Theta + cos\Theta + cos(90 - \Theta) = 1$

$2cos\Theta + cos\Theta = 1$

$3cos\Theta = 1$

$cos\Theta = \frac {1}{3}$ ""(a)

Also $2cos\Theta + sin \Theta = 1$

$2sin (90 - \Theta) + sin\Theta = 1$

$2sin\Theta + sin\Theta = 1$

$3sin\Theta = 1$

$sin\Theta = \frac {1}{3}$ ""(b)

Now,using (a)& (b)-

$7cos\Theta + 6sin\Theta = 7\times\frac {1}{3} + 6\times \frac {1}{3}$

= $\frac {7}{3} + \frac {6}{3}$

= $\frac {13}{3}$