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TS EAMCET · Maths · Trigonometric Equations

If \(\cos x+\cos y=\frac{2}{3}\) and \(\sin x-\sin y=\frac{3}{4}\) then \(\sin (x-y)+\cos (x-y)=\)

  1. A \(\frac{161}{145}\)
  2. B \(\frac{127}{145}\)
  3. C \(\frac{1}{2}\)
  4. D \(\frac{8}{9}\)
Verified Solution

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…