AP EAMCET · Maths · Differential Equations
The solution of \(\tan y \frac{d y}{d x}=\sin (x+y)+\sin (x-y)\) is
- A \(\sec y=2 \cos x+c\)
- B \(\sec y=-2 \cos x+c\)
- C \(\tan y=-2 \cos x+c\)
- D \(\sec ^2 y=-2 \cos x+c\)
Answer & Solution
Correct Answer
(B) \(\sec y=-2 \cos x+c\)
Step-by-step Solution
Detailed explanation
\(\tan y \frac{d y}{d x}=\sin (x+y)+\sin (x-y)\) \(\tan y \frac{d y}{d x}=2 \cdot \sin \left(\frac{2 x}{2}\right) \cdot \cos \left(\frac{2 y}{2}\right)\) \(\left[\because \sin C+\sin D=2 \sin \left(\frac{C+D}{2}\right) \cdot \cos \left(\frac{C-D}{2}\right)\right]\)…
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