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Trigonometric Ratio and Identites question

2004 · Shift 0 · Q95

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JEE Main
Mathematics
Trigonometric Ratio and Identites
2004 · Shift 0 · Q95

Trigonometric Ratio and Identites question

2004 · Shift 0 · Q95

JEE MainMathematicsTrigonometric Ratio and IdentitesMCQ+4 / −1

Let

\alpha ,\,\beta

be such that

\pi \lt \alpha - \beta \lt 3\pi

. If

sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}

and

\cos \alpha + \cos \beta = - {{27} \over {65}}

then the value of

\cos {{\alpha - \beta } \over 2}

:

A
${{ - 6} \over {65}}\,\,$
B
${3 \over {\sqrt {130} }}$
C
${6 \over {65}}$
D
$- {3 \over {\sqrt {130} }}$

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