cotA-tanA = 2cos^A-1/sinAcosA
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Let c=cos A ,s=sin A then cotA=c/s, tanA=s/c and the problem becomes:
c/s -s/c =(2c^2 -1)/sc
Now c/s-s/c =c^2/sc -s^2/sc =(c^2-s^2)/sc
Also, c^2+s^2=1 so c^2-s^2 =2c^2 -c^2 -s^2 =2c^2 -1
Hence indeed we see that the left hand side (c/s-s/c) can be rewritten as ([2c^2-1]/sc) i.e. the left hand side.
c/s -s/c =(2c^2 -1)/sc
Now c/s-s/c =c^2/sc -s^2/sc =(c^2-s^2)/sc
Also, c^2+s^2=1 so c^2-s^2 =2c^2 -c^2 -s^2 =2c^2 -1
Hence indeed we see that the left hand side (c/s-s/c) can be rewritten as ([2c^2-1]/sc) i.e. the left hand side.
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