Question #d17b0

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Answer 1 · 2017-02-16T19:59:36

combine the $L H S$ $LHS$ using the rule of fractions. So find a common denominator then simplify

$\frac{sin u + cos u}{cos u} - \frac{sin u - cos u}{sin u}$ $(sinu+cosu)/cosu-(sinu-cosu)/sinu$

$\frac{sin u (sin u + cos u)}{sin u cos u} - \frac{cos u (sin u - cos u)}{cos u sin u}$ $(sinu(sinu+cosu))/(sinucosu)-(cosu(sinu-cosu))/(cosusinu)$

multiply the numerators out and put over the common denominator.

$\frac{({sin}^{2} u + sin u cos u) - (sin u cos u - {cos}^{2} u)}{sin u cos u}$ $((sin^2u+sinucosu)-(sinucosu-cos^2u))/(sinucosu)$

now simplify

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

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

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

so we have:

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

$=cscxsecx " as required."$