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Question Bank [2022] — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsQuestion Bank [2022]2 Marks
Question
$\int \frac{\sin (x-a)}{\cos (x+ b )} d x$
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Answer

$\text { Let } I =\int \frac{\sin (x- a )}{\cos (x+ b )} d x$
$=\int \frac{\sin [(x+ b )-( a + b )]}{\cos (x+b) d x}$
$=\int \frac{\sin (x+ b ) \cdot \cos ( a + b )-\cos (x+ b ) \cdot \sin ( a + b )}{\cos (x+ b )} d x$
$=\int\left[\frac{\sin (x+ b ) \cdot \cos ( a + b )}{\cos (x+ b )}-\frac{\cos (x+ b ) \cdot \sin ( a + b )}{\cos (x+ b )}\right] d x$
$=\int[\tan (x+ b ) \cdot \cos ( a + b )-\sin ( a + b )] d x$
$=\cos ( a + b ) \int \tan (x+ b ) \cdot d x-\sin ( a + b ) \int d x$
$\therefore I =\cos ( a + b ) \cdot \log |\sec ( x + b )|-[\sin ( a + b )] x + c $

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