JEE MATHEMATICS MCQ: MULTIPLE AND SUBMULTIPLE ANGLES

1 Easy

1 of 1

Application +4 | -1

Let

\alpha ,\,\beta

be such that

\pi < \alpha - \beta < 3\pi

. If

\sin \,\,\alpha + \sin \beta = - \frac{{21}}{{65}}

and

\cos \,\,\alpha + \cos \,\,\beta = - \frac{{27}}{{65}}

, then the value of

\cos \,\,\frac{{\left( {\alpha - \beta } \right)}}{2}

View answer and explanation

Correct option: A

- \frac{3}{{\sqrt {130} }}

Option A (

- \frac{3}{{\sqrt {130} }}

) is correct because, after squaring and adding the given equations and using trigonometric identities, we find the value of

\cos \frac{{\left( {\alpha - \beta } \right)}}{2}

considering the given range of

\alpha - \beta

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