Wie beweisen Sie # (1-sin ^ 2theta) (1 + cot ^ 2theta) = cot ^ 2theta #?

Wir wissen das ,

#(1)cos^2x+sin^2x=1#
#(2)csc^2x-cot^2x=1#
#(3)cscx=1/sinx#
#(4)cosx/sinx=cotx#

Mit #(1) and (2):#

#LHS=(1-sin^2theta)(1+cot^2theta)#

#LHS=cos^2thetacsc^2thetatoApply(3)#

#LHS=cos^2theta*1/sin^2theta#

#LHS=cos^2theta/sin^2thetatoApply(4)#

#LHS=cot^2theta#

#LHS=RHS#