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Find ∫ Sin ( X − a ) Sin ( X + a ) D X - Mathematics

Question

Sum

Find `int_  sin ("x" - a)/(sin ("x" + a )) d"x"`

Solution

Let I = `int_  sin("x" - a)/sin ("x" + a)d"x"`

⇒ I = `int_  sin [("x" + a) - 2a]/sin ("x" + a)d"x"`

= `int_  (sin ("x" + a )·cos (2a) - cos ("x" + a)· sin (2a))/sin ("x" + a)d"x"`  

= `int_  cos (2a) d"x" - int_  cot ("x" + a)· sin (2a)d"x"`

= x·cos (2a) - log|sin (x + a)|·sin (2a) + C

  Is there an error in this question or solution?
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