Question

If cos theta : Sin theta = 1 : 2 then find the value of 8 cos theta - 2 sin theta by 4 cos theta + 2 Sin Theta

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Answer 1

Answer: 1/2

Step by step explanation:-

Answer 2

The value of the given expression is 1/2

Step-by-step explanation:

It has been given that

cos theta : Sin theta = 1 : 2

Mathematically, we can write it as

$\frac{\cos\theta}{\sin\theta}=\frac{1}{2}$

Now, the given expression is

$\frac{8\cos\theta-2\sin\theta}{4\cos\theta+2\sin\theta}$

Take 2 sinФ common from numerator and denominator

$\frac{2\sin\theta(4\frac{\cos\theta}{\sin\theta}-1)}{2\sin\theta(2\frac{\cos\theta}{\sin\theta}+1)}$

Cancel the common term from numerator and denominator

$\frac{4\frac{\cos\theta}{\sin\theta}-1}{2\frac{\cos\theta}{\sin\theta}+1}$

Substituting the given value

$\frac{4\cdot\frac{1}{2}-1}{2\cdot\frac{1}{2}+1}\\\\=\frac{2-1}{1+1}\\\\=\frac{1}{2}$

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