if cot thetha= 4/3 then the value of cos thetha - sin thetha ÷ cos thetha+ sin thetha
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if cot thetha= 4/3 then the value of cos thetha - sin thetha ÷ cos thetha+ sin thetha
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Answer:
Let's denote θ as the angle in radians.
Given that cot(θ) = 4/3, we can use trigonometric identities to find the values of cos(θ) and sin(θ).
cot(θ) = 4/3 can be rewritten as cos(θ)/sin(θ) = 4/3.
This implies that cos(θ) = 4x and sin(θ) = 3x, where x is a positive constant.
Now, we can calculate the value of the expression:
cos(θ) - sin(θ) ÷ cos(θ) + sin(θ)
= (4x - 3x) ÷ (4x + 3x)
= x ÷ 7x
= 1/7
So, if cot(θ) = 4/3, then the value of cos(θ) - sin(θ) ÷ cos(θ) + sin(θ) is 1/7.
Explanation:
Given that cot(θ) = 4/3, we can find the values of cos(θ) and sin(θ) first:
cot(θ) = 4/3
This implies that:
cos(θ) = 3/4
sin(θ) = 4/5
Now, we can calculate the expression:
(cos(θ) - sin(θ)) / (cos(θ) + sin(θ))
Substitute the values of cos(θ) and sin(θ):
= (3/4 - 4/5) / (3/4 + 4/5)
To simplify:
= [(15 - 16) / 20] / [(15 + 16) / 20]
= (-1/20) / (31/20)
Now, divide:
= -1/31
So, the value of the expression is -1/31.