COMEDK · Maths · 8. Trigonometric Ratios & Identities
If \(\sin A+\sin B=a\) and \(\cos A+\cos B=b\), then \(\cos (A+B)\) equals?
- A \(\dfrac{a^2+b^2}{b^2-a^2}\)
- B \(\dfrac{2 a b}{a^2+b^2}\)
- C \(\dfrac{b^2-a^2}{a^2+b^2}\)
- D \(\dfrac{a^2-b^2}{a^2+b^2}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{b^2-a^2}{a^2+b^2}\)
Step-by-step Solution
Detailed explanation
Given \(\sin A + \sin B = a\) and \(\cos A + \cos B = b\). Squaring both equations: \((\sin A + \sin B)^2 = a^2 \Rightarrow \sin^2 A + \sin^2 B + 2 \sin A \sin B = a^2\) \((\cos A + \cos B)^2 = b^2 \Rightarrow \cos^2 A + \cos^2 B + 2 \cos A \cos B = b^2\) Adding the two squared…
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