Question #3104b

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Answer 1 · 2016-06-07T20:30:37

C) #sin(x)/cos(x)+cos(x)/sin(x)=csc(x)sec(x)#

#sin(x)/cos(x)+cos(x)/sin(x)#

(Multiply by #sin(x)/sin(x)# and #cos(x)/cos(x)# to give terms a common denominator)

#= sin^2(x)/(sin(x)cos(x))+cos^2(x)/(sin(x)cos(x))#

#=(sin^2(x)+cos^2(x))/(sin(x)cos(x))#

(Apply the identity #sin^2(x)+cos^2(x)=1#)

#=1/(sin(x)cos(x))#

#=1/sin(x)*1/cos(x)#

(Apply the definitions #csc(x)=1/sin(x)# and #sec(x)=1/cos(x)#)

#=csc(x)sec(x)#

#=sec(x)csc(x)#

Thus the answer is C.