Verify? $2cosx-secx=cosx-tanx/cscx$

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Answer 1 · 2017-03-29T04:42:06

See below:

$2cosx-secx=cosx-tanx/cscx$

$2cosx-1/cosx=cosx-(sinx/cosx)/(1/sinx)$

$2cosx-1/cosx=cosx-(sinx/cosx)xx(sinx)$

$2cosx-1/cosx=cosx-sin^2x/cosx$

$(2cos^2x)/cosx-1/cosx=cos^2x/cosx-sin^2x/cosx$

$(2cos^2x-1)/cosx=(cos^2x-sin^2x)/cosx$

Use $color(blue)(sin^2x+cos^2x=1)=>color(red)(sin^2x=1-cos^2x$

$(2cos^2x-1)/cosx=(cos^2x-(1-cos^2x))/cosx$

$(2cos^2x-1)/cosx=(cos^2x-1+cos^2x)/cosx$

$(2cos^2x-1)/cosx=(2cos^2x-1)/cosx$

Verify? 2cosx-secx=cosx-tanx/cscx2cosx-secx=cosx-tanx/cscx