How do you prove #secx - cosx = tanx * sinx#?

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How do you prove #secx - cosx = tanx * sinx#?

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Answer 1 · 2016-05-02T21:40:31

Using the definitions #sec(x)=1/cos(x)# and #tan(x)=sin(x)/cos(x)# along with the identity #sin^2(x)+cos^2(x)=1 => sin^2(x)=1-cos^2(x)#,
for #cos(x)!=0# we have

#sec(x)-cos(x) = 1/cos(x)-cos^2(x)/cos(x)#

#=(1-cos^2(x))/cos(x)#

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

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

#=tan(x)*sin(x)#

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How do you prove #secx - cosx = tanx * sinx#?

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