How do you simplify #sin(-x)/cos(-x)#?

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Answer 1 · 2017-01-13T15:33:24

#-tanx#

#cosx# is an even function. This means that #cos(-x)=cosx#

#sinx# is an odd function. This means that #sin(-x)=-sinx#

#sin(-x)/cos(-x)=-sinx/cosx=-tanx#

Answer 2 · 2017-01-13T15:36:52

This will be equal to #-tan(x)#

Because it is an even function, #cos(-x)=cos(x)#

Similarly, because it is an odd function, #sin(-x)=-sin(x)

So, the above ratio can be written

#-sin(x)/cos(x)# which is equal to #-tan(x)#