If ∫ ( sin x/ sin (x-α)) d x=A x+ B log sin (x-α)+C, then value of ( A , B ) is

Question

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

Tardigrade Admin · Accepted Answer

∫ ( sin x/ sin (x-α)) d x =∫ ( sin (x-α+α)/ sin (x-α)) d x =∫ ( sin (x-α) cos α+ cos (x-α) sin α/ sin (x-α)) d x =∫ cos α+ sin α cot (x-α) d x =( cos α) x+( sin α) log sin (x-α)+C A= cos α, B= sin α

Q. If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α) + C$ , then value of $(A, B)$ is

$(- cos α, sin α)$

$(cos α, sin α)$

$(- sin α, cos α)$

$(sin α, cos α)$

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

(−cosα,sinα)

(cosα,sinα)

(−sinα,cosα)

(sinα,cosα)

∫sin(x−α)sinx​dx =∫sin(x−α)sin(x−α+α)​dx =∫sin(x−α)sin(x−α)cosα+cos(x−α)sinα​dx =∫{cosα+sinαcot(x−α)}dx =(cosα)x+(sinα)logsin(x−α)+C A=cosα,B=sinα

Q. If $\int \frac{s i n x}{s i n ( x - α )} d x = A x + B lo g sin (x - α) + C$ , then value of $(A, B)$ is

$(- cos α, sin α)$

$(cos α, sin α)$

$(- sin α, cos α)$

$(sin α, cos α)$