TS EAMCET · Maths · Trigonometric Equations
If \(\cos x+\cos y=\frac{2}{3}\) and \(\sin x-\sin y=\frac{3}{4}\) then \(\sin (x-y)+\cos (x-y)=\)
- A \(\frac{161}{145}\)
- B \(\frac{127}{145}\)
- C \(\frac{1}{2}\)
- D \(\frac{8}{9}\)
Answer & Solution
Correct Answer
(B) \(\frac{127}{145}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \cos x+\cos y=\frac{2}{3} \\ & \Rightarrow 2 \cos \frac{x+y}{2} \cdot \cos \left(\frac{x-y}{2}\right)=\frac{2}{3} \quad ....\mathrm{(i)} \\ & \sin x-\sin y=\frac{3}{4} \\ & \Rightarrow 2 \cos \frac{x+y}{2} \cdot \sin \left(\frac{x-y}{2}\right)=\frac{3}{4} \quad…
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