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Trigonometric Functions and Equations question

2022 · Shift 2 · Q19

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JEE Advanced
Mathematics
Trigonometric Functions and Equations
2022 · Shift 2 · Q19

Trigonometric Functions and Equations question

2022 · Shift 2 · Q19

JEE AdvancedMathematicsTrigonometric Functions and EquationsNumerical+3 / −1

Let

\alpha

and

\beta

be real numbers such that

-\frac{\pi}{4}\lt \beta\lt 0\lt \alpha\lt \frac{\pi}{4}

. If

\sin (\alpha+\beta)=\frac{1}{3}

and

\cos (\alpha-\beta)=\frac{2}{3}

, then the greatest integer less than or equal to

\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^{2}

is

Numerical answer

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