Question #d17b0

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Answer 1 · 2017-02-16T19:59:36

combine the #LHS# using the rule of fractions. So find a common denominator then simplify

#(sinu+cosu)/cosu-(sinu-cosu)/sinu#

#(sinu(sinu+cosu))/(sinucosu)-(cosu(sinu-cosu))/(cosusinu)#

multiply the numerators out and put over the common denominator.

#((sin^2u+sinucosu)-(sinucosu-cos^2u))/(sinucosu)#

now simplify

#(sin^2u+cancel(sinucosu-sinucosu)+cos^2u)/(sinucosu)#

#(sin^2u+cos^2u)/(sinucosu)#

#" but "sin^2u+cos^2u=1#

so we have:

#(sin^2u+cos^2u)/(sinucosu)=1/(sinucosu)=1/sinuxx1/cosu#

#=cscxsecx " as required."#