if cot thetha= 4 then the value of cos thetha - sin thetha ÷ cos thetha+ sin thetha
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if cot thetha= 4 then the value of cos thetha - sin thetha ÷ cos thetha+ sin thetha
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To find the value of (cos θ - sin θ) / (cos θ + sin θ), we can use the given information that cot θ =4.
We know that cot θ = cos θ / sin θ. So, we can rewrite cot θ =4 as:
cos θ / sin θ =4Cross-multiplying, we get:
cos θ =4 sin θNow, let's substitute this value of cos θ into the expression (cos θ - sin θ) / (cos θ + sin θ):
(4 sin θ - sin θ) / (4 sin θ + sin θ)
Simplifying the numerator and denominator:
3 sin θ /5 sin θThe sin θ terms cancel out:
3 /5Therefore, the value of (cos θ - sin θ) / (cos θ + sin θ) when cot θ =4 is3/5.
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To find the value of (cos theta - sin theta) / (cos theta + sin theta) given that cot theta = 4, we can use trigonometric identities to express the expression in terms of cot theta.
First, let's express cos theta and sin theta in terms of cot theta:
cos theta = 1 / sqrt(1 + cot^2 theta)
sin theta = cot theta / sqrt(1 + cot^2 theta)
Substituting these values into the expression, we get:
(cos theta - sin theta) / (cos theta + sin theta) = (1 / sqrt(1 + cot^2 theta) - cot theta / sqrt(1 + cot^2 theta)) / (1 / sqrt(1 + cot^2 theta) + cot theta / sqrt(1 + cot^2 theta))
Simplifying the expression further:
= (1 - cot theta) / (1 + cot theta)
Since we are given that cot theta = 4, we can substitute this value into the expression:
= (1 - 4) / (1 + 4)
= -3 / 5
Therefore, the value of (cos theta - sin theta) / (cos theta + sin theta) when cot theta = 4 is -3/5.