tanx=−512,x lies in second quadrant.
tanx=−512
⇒cotx=1tanx=−125
Now using, 1+tan2x=sec2x
⟹sec2x=1+25144=169144
⟹secx=±1312
Since x lies in second quadrant, the value of secx will be negative.
∴secx=−1312
cosx=1secx=−1213
tanx=sinxcosx
⟹sinx=(−512)×(−1213)=513
∴cscx=1sinx=135