Question 924905
Prove the following: (sec(x)-cos(x))(csc(x)-sin(x))=tan(x)/1+tan^2(x) .do only one side please. Thank you in advance. I apologize for sending this twice, the first time instead of '1' I wrote 'a'.
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{{{(secx-cosx)(cscx-sinx)=tanx/(1+tan^2(x))}}}
start with left side:
{{{(secx-cosx)(cscx-sinx)
=((1/cosx)-cosx)((1/sinx)-sinx)
=((1-cos^2(x))/cos(x))((1-sin^2(x))/sin(x))
=(sin^2(x)/cosx)(cos^2(x)/sinx)}}}
{{{tanxcos^2(x)=tanx/sec^2(x)=tanx/(1+tan^2(x))}}}
verified: left side =right side