(x+cos x)(x-tan x)?

1 Answer
Hammer
Jun 7, 2018

#(x+cosx)(x-tanx)=x^2-xsinx"/"cosx+xcosx-sinx#

Explanation:

Let us expand this product

#(x+cosx)(x-tanx)=x(x-tanx)+cosx(x-tanx)=x^2-xtanx+xcosx-cosxtanx#

Remember that #tanx=sinx"/"cosx#, hence

#cosxtanx=cancelcosxsinx/cancelcosx=sinx#

#xtanx=xsinx/cosx#

So the answer seek is

#color(red)((x+cosx)(x-tanx)=x^2-xsinx"/"cosx+xcosx-sinx#

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