TS EAMCET · Maths · Definite Integration
If \(f(x, y)=\frac{\cos (x-4 y)}{\cos (x+4 y)}\), then \(\left.\frac{\partial f}{\partial x}\right|_{y=\frac{x}{2}}\) is equal to :
- A -1
- B 0
- C 1
- D 2
Answer & Solution
Correct Answer
(B) 0
Step-by-step Solution
Detailed explanation
\(\because \quad f(x, y)=\frac{\cos (x-4 y)}{\cos (x+4 y)}\) \(\therefore \quad f\left(x, \frac{\pi}{2}\right)=\frac{\cos (x-2 \pi)}{\cos (x+2 \pi)}\) \(=\frac{\cos (2 \pi-x)}{\cos (2 \pi+x)}=\frac{\cos x}{\cos x}=1\) \(\therefore \quad \frac{\partial f}{\partial x}=0\)
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