AP EAMCET · Maths · Trigonometric Equations
If \(\cos \alpha+\cos \beta=\frac{1}{3}\) and \(\sin \alpha+\sin \beta=\frac{1}{4}\), then \(\cos (\alpha+\beta)=\)
- A \(\frac{24}{25}\)
- B \(\frac{7}{25}\)
- C \(\frac{13}{25}\)
- D \(\frac{12}{13}\)
Answer & Solution
Correct Answer
(B) \(\frac{7}{25}\)
Step-by-step Solution
Detailed explanation
Given \(\cos \alpha+\cos \beta=\frac{1}{3}\) \[ \Rightarrow 2 \cos \left(\frac{\alpha+\beta}{2}\right) \cos \left(\frac{\alpha-\beta}{2}\right)=\frac{1}{3}.....(i) \] \(\& \sin \alpha+\sin \beta=\frac{1}{4}\)…
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