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Let a and b be unknown nonzero constants such that the equation below (September 2023 - G01)
Updated on 05/30/2024
Let a and b be unknown nonzero constants such that the equation below is true for all values of θ.
a sin^2 θ + a cos^2 θ = b
What is the value of b/a?
F. -1
G. 0
H. 1/2
J. 1
K. 2
Solution
Correct answer: J. 1.
To solve this problem, we can start by expanding the left-hand side of the equation:
asin^2θ + acos^2θ = b
Using the trigonometric identity sin^2θ + cos^2θ = 1, we can rewrite the equation as:
a(1 - cos^2θ) + a cos^2θ = b
Combine like terms:
a(1 - cos^2θ + cos^2θ) = b
Simplify:
a = b
So, the value of b/a is:
b/a = 1
Exam Edition: September 2023 - G01
Exam Year: 2023
Related topics: Trigonometry, Algebra
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