If 4 tanθ = 3, then (4sinθ − cosθ)/(4sinθ + cosθ) is equal to
a. 2/3
b. 1/3
c. 1/2
d. 3/4
Solution:
Given, 4 tanθ = 3
We have to find the value of (4sinθ - cosθ)/(4sinθ + cosθ)
Now, tanθ = 3/4
We know that tan A = opposite / adjacent
Opposite = 3
Adjacent = 4
Using the pythagorean theorem,
(hypotenuse)² = (opposite)² + (adjacent)²
(hypotenuse)² = (3)² + (4)²
(hypotenuse)² = 9 + 16
(hypotenuse)² = 25
Taking square root,
Hypotenuse = 5
We know that sin A = opposite/hypotenuse
So, sinθ = 3/5
We know that cos A = adjacent / hypotenuse
So, cosθ = 4/5
Now, (4sinθ - cosθ) = 4(3/5) - (4/5)
= 12/5 - 4/5
= (12 - 4)/5
= 8/5
Now, (4sinθ + cosθ) = 4(3/5) + (4/5)
= 12/5 + 4/5
= (12 + 4)/5
= 16/5
So, (4sinθ - cosθ)/(4sinθ + cosθ) = (8/5) / (16/5)
= 8(5) / 16(5)
= 8/16
= 1/2
✦ Try This: If 4 sinθ = 3, then (4cosθ - cotθ)/(4cosθ + cotθ) is equal to
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 8
NCERT Exemplar Class 10 Maths Exercise 8.1 Problem 12
If 4 tanθ = 3, then (4sinθ − cosθ)/(4sinθ + cosθ) is equal to a. 2/3, b. 1/3, c. 1/2, d. 3/4
Summary:
If 4 tanθ = 3, then (4sinθ - cosθ)/(4sinθ + cosθ) is equal to 1/2
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