Question

if cos theta is equals to 1 by root 2 then find the value of 4 + cot theta​

Answer 1

Answer:

5

Step-by-step explanation:

cos@= 1/√2

@=45°

Therefore,

4 + cot@ = 4+1 = 5

Answer 2

The value of 4 + cot theta​ is 5

Solution:

Given that,

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

To find: value of 4 + cot theta

$cot\ \theta = \frac{adjacent}{opposite}$

We know that,

$cos\ \theta = \frac{adjacent}{hypotenuse}$

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

Therefore,

$adjacent = 1\\\\hypotenuse = \sqrt{2}\\\\By\ pythogoras\ theorem\\\\hypotenuse^2 = opposite^2+adjacent^2\\\\(\sqrt{2})^2 = opposite^2+ 1\\\\2 = opposite^2+ 1\\\\opposite^2 = 2 - 1\\\\opposite^2 = 1\\\\opposite = 1$

Therefore,

$cot\ \theta = \frac{adjacent}{opposite}\\\\cot\ \theta = \frac{1}{1}\\\\cot\ \theta = 1$

Thus,

$4 + cot\ \theta = 4 + 1 = 5$

Thus value of 4 + cot theta​ is 5

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