If ∫ (sin x/sin (x-α)) dx = Ax + Blogsin(x-α) + C, then value of (A, B) is

Question

If ∫ (sin x/sin (x-α)) dx = Ax + Blogsin(x-α) + C, then value of (A, B) is (A) (sin α, cos α) (B) (cos α, sin α) (C) (- sin α cos α) (D) (- cos α, sin α)

Tardigrade Admin · Accepted Answer

Put x - Î± = t ⇒ ∫ (sin(α+ t)/sin t) dt sin α ∫ cot tdt + cos α ∫ dt = cos Î±(x â Î±) + sin Î± ln |sin t |+c A = cos Î±, B = sin Î±

Q. If $\int \frac{s in x}{s in ( x - α )} d x = A x + Bl o g s in (x - α) + C$ , then value of $(A, B)$ is

$(s in α, cos α)$

$(cos α, s in α)$

$(- s in α cos α)$

$(- cos α, s in α)$

Put $x - α = t$
$\Rightarrow \int \frac{s in ( α + t )}{s in t} d t s in α \int co t t d t + cos α \int d t$
$= cos α (x - α) + s in α l n ∣ s in t ∣ + c$
$A = cos α, B = s in α$

Q. If ∫sin(x−α)sinx​dx=Ax+Blogsin(x−α)+C, then value of (A,B) is

(sinα,cosα)

(cosα,sinα)

(−sinαcosα)

(−cosα,sinα)