solve 1/1+cosx=csc^2x-cscxcotx

prove the following trig equation

 

1/(1+cosx)=csc^62-cscxcotx
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1 Answer

csc2(x)-csc(x)cot(x)=csc(x)(csc(x)-cot(x))=

(1/sin(x)-cos(x)/sin(x))/sin(x)=(1-cos(x))/sin2(x)=

(1-cos(x))/(1-cos2(x))=(1-cos(x))/[(1-cos(x))(1+cos(x))]=

1/(1+cos(x)).

Therefore 1/(1+cos(x)=csc2(x)-csc(x)cot(x) QED

by Top Rated User (1.2m points)

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