∫(1-cosx)cosec2xdx=
tanx2+c
–cotx2+c
2tanx2+c
–2cotx2+c
Explanation for the correct answer:
Given
∫(1-cosx)cosec2xdx=∫(1–cosx)sin2xdx=∫(1–cosx)(1–cos2x)dx∵sin2x=1–cos2x=∫(1–cosx)(1+cosx)(1-cosx)dx∵a2-b2=a+ba-b=∫1(1+cosx)dx=∫dx1+2cos2x2–1∵cosx=2cos2x2–1=∫sec2x2dxI=tanx2+c∵∫sec2x2dx
Therefore, ∫(1-cosx)cosec2xdx=tan(x2)+c
Hence, the correct answer is option (A).