JEE MATHEMATICS MCQ: TRIGONOMETRIC EQUATIONS

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Analyzing +4 | -1

\alpha

and

\beta

satisfy the equation

12 \sin \alpha+5 \cos \alpha

=2 \beta^2-8 \beta+21

, then the value of

\beta^2-2 \beta

is _____.

View answer and explanation

Correct option: A

Option A (0) is correct because the maximum value of

12 \sin \alpha + 5 \cos \alpha

is 13, and the minimum value of

2 \beta^2 - 8 \beta + 21

is also 13, which occurs when

\beta = 2

. Therefore,

\beta^2 - 2\beta = 0

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