If In=∫cosecn⁡xdx then 9I10−8I8 is equal to

I10=∫cosec10xdx=∫cosec8⁡xcosec2⁡xdx=cos⁡ec8x(−cot⁡x)−∫8cosec7⁡x(−cosec⁡xcot⁡x)(−cot⁡x)dx=−cosec8⁡xcot⁡x−8∫cosec8⁡xcosec2⁡x−1dxI10=−cosec8⁡xcot⁡x−8∫cosec10⁡xdx+8∫cosec8⁡xdx=−cosec8⁡xcot⁡x−8I10+8I89I10−8I8=−cosec8⁡xcot⁡x+C