COMEDK · Maths · 8. Trigonometric Ratios & Identities
If \(\sin A+\sin B=-\dfrac{21}{65}, \cos A+\cos B=-\dfrac{27}{65}\) and \(\pi < A-B < 3 \pi\), then the value of \(\cos \left(\dfrac{A-B}{2}\right)\) is
- A \(\dfrac{6}{65}\)
- B \(\dfrac{3}{\sqrt{130}}\)
- C \(-\dfrac{3}{\sqrt{130}}\)
- D \(-\dfrac{6}{65}\)
Answer & Solution
Correct Answer
(C) \(-\dfrac{3}{\sqrt{130}}\)
Step-by-step Solution
Detailed explanation
Given \(\sin A + \sin B = -\dfrac{21}{65}\) and \(\cos A + \cos B = -\dfrac{27}{65}\). Using sum-to-product formulas: \(2 \sin \left(\dfrac{A+B}{2}\right) \cos \left(\dfrac{A-B}{2}\right) = -\dfrac{21}{65}\) (1)…
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