CUET · MATHS · PYQ PAPER 2023
\(\int \frac{d x}{1+\tan x}\) is equal to:
- A \(\frac{x}{2}+\frac{1}{2} \log |\cos x-\sin x|+c\)
- B \(\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c\)
- C \(\frac{x}{2}-\frac{1}{2} \log |\cos x-\sin x|+c\)
- D \(\frac{x}{2}-\frac{1}{2} \log |\cos x+\sin x|+c\)
Answer & Solution
Correct Answer
(B) \(\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c\)
Step-by-step Solution
Detailed explanation
\( \int \frac{d x}{1+\tan x} = \int \frac{\cos x}{\cos x+\sin x} dx \) \( \cos x = A(\cos x+\sin x) + B(\cos x-\sin x) \Rightarrow A=\frac{1}{2}, B=\frac{1}{2} \)…
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