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#