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CBSE Class 12 Math 2023 All Sets Solved Paper

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Question : 9 of 20
Marks: +1, -0
Anti-derivative of tan⁡x−1tan⁡x+1\frac{\tan x - 1}{\tan x + 1} with respect to x is:
Solution:  
I = ∫tan⁡x−1tan⁡x+1 dx\int \frac{\tan x - 1}{\tan x + 1} \, dx
=−∫1−tan⁡x1+tan⁡x dx= -\int \frac{1 - \tan x}{1 + \tan x} \, dx
=−∫tan⁡(π4−x) dx= -\int \tan\left(\frac{\pi}{4} - x\right) \, dx
=ln⁡∣sec⁡(π4−x)∣+c= \ln \left| \sec\left(\frac{\pi}{4} - x\right) \right| + c
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