If #sin A sin B - cos A cos B + 1 = 0#, how do you prove that # 1 + cot A tan B = 0#?

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Answer 1 · 2017-09-27T15:05:11

#sin A sin B - cos A cos B + 1 = 0

#=>cos A cos B -sin A sin B = 1

#=>cos (A + B) = 1 =cos0#

#=>A=2npi-B, " where " n in ZZ#

Now

#1+cotAtanB#

#=>1+cot(2npi-B)tanB#

#=>1-cot(B)tanB=1-1=0#