JEE Main 2004Annual, Paper 1MathematicsMediumTrigonometry118× since 2002Let α, β\alpha ,\,\betaα,β be such that π<α−β<3π\pi < \alpha - \beta < 3\piπ<α−β<3π. If sin α+sinβ=−2165sin{\mkern 1mu} \alpha + \sin \beta = - {{21} \over {65}}sinα+sinβ=−6521 and cosα+cosβ=−2765\cos \alpha + \cos \beta = - {{27} \over {65}}cosα+cosβ=−6527 then the value of cosα−β2\cos {{\alpha - \beta } \over 2}cos2α−β :AOption A. −665 {{ - 6} \over {65}}\,\,65−6BOption B. 3130{3 \over {\sqrt {130} }}1303COption C. 665{6 \over {65}}656DOption D. −3130- {3 \over {\sqrt {130} }}−1303CheckSkip · show solution
