Simplify ? # (cos^2a - sin^2b)/(sin^2a • sin^2b) - ctg^2a • ctg^2b #

1 Answer
Øko
Apr 5, 2018

#(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-cot^2(a)cot^2(b)=-1#

Explanation:

We want to simplify

#(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-cot^2(a)cot^2(b)#

We will use the identity

  • #sin^2(x)+cos^2(x)=1#

Thus

#(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-cot^2(a)cot^2(b)#

#(cos^2(a)-sin^2(b))/(sin^2(a)sin^2(b))-(cos^2(a)cos^2(b))/(sin^2(a)sin^2(b))#

#(cos^2(a)-sin^2(b)-cos^2(a)cos^2(b))/(sin^2(a)sin^2(b))#

#(cos^2(a)(1-cos^2(b))-sin^2(b))/(sin^2(a)sin^2(b))#

#(cos^2(a)sin^2(b)-sin^2(b))/(sin^2(a)sin^2(b))#

#(-sin^2(b)(1-cos^2(a)))/(sin^2(a)sin^2(b))#

#(-sin^2(b)sin^2(a))/(sin^2(a)sin^2(b))#

#-1#

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