How do I prove $(sec x/cos x)+(csc x/sin x)=4 csc^2(2x)$ ?

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Answer 1 · 2017-11-21T08:46:26

Please refer to the explanation below for proof .

$LHS=secx/cosx+cscx/sinx$

$=(1/cosx)/cosx+(1/sinx)/sinx$

$=1/cos^2x+1/sin^2x$

$=(sin^2x+cos^2x)/(sin^2x*cos^2x$

$=1/(sin^2x*cos^2x)*4/4$

$=4/(2sinx*cosx)^2$

$=4/sin^2(2x)=4csc^2(2x)=RHS$

How do I prove (sec x/cos x)+(csc x/sin x)=4 csc^2(2x)(sec x/cos x)+(csc x/sin x)=4 csc^2(2x)?