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Maths-

General

Easy

Question

If $not stretchy integral fraction numerator sin invisible function application x over denominator sin invisible function application left parenthesis x minus alpha right parenthesis end fraction$ dx = Ax + B log sin (x – ) + c then value of (A, B) is

(– sin $α$ , cos $α$ )
(cos $α$ , sin $α$ )
(sin $α$ , cos $α$ )
(– cos $α$ , sin $α$ )

The correct answer is: (cos $alpha$ , sin $alpha$ )

$not stretchy integral fraction numerator sin invisible function application left parenthesis x minus alpha plus alpha right parenthesis over denominator sin invisible function application left parenthesis x minus alpha right parenthesis end fraction$ dx
= $not stretchy integral fraction numerator sin invisible function application left parenthesis x minus alpha right parenthesis cos invisible function application alpha plus cos invisible function application left parenthesis x minus alpha right parenthesis sin invisible function application alpha over denominator sin invisible function application left parenthesis x minus alpha right parenthesis end fraction$ dx
= cos  $not stretchy integral d x plus sin invisible function application alpha not stretchy integral cot invisible function application left parenthesis x minus alpha right parenthesis d x$
= (cos ) x + sin . log {sin (x – )} + c

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