How do you multiply and simplify $tan x (cos x - csc x)$ $tanx(cosx-cscx)$ ?

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Answer 1 · 2016-09-25T09:55:20

$tan x (cos x - csc x) = sin x - sec x$ $tanx(cosx-cscx)=sinx-secx$

$tan x (cos x - csc x)$ $tanx(cosx-cscx)$

= $\frac{sin x}{cos x} (cos x - \frac{1}{sin x})$ $sinx/cosx(cosx-1/sinx)$

= $\frac{sin x}{cos x} \times cos x - \frac{sin x}{cos x} \times \frac{1}{sin x}$ $sinx/cosx xxcosx-sinx/cosx xx1/sinx$

= $sinx/cancel(cosx) xxcancel(cosx)-cancel(sinx)/cosx xx1/cancel(sinx)$

= $sinx-secx$

How do you multiply and simplify tanx(cosx-cscx)tanx(cosx−cscx)tanx(cosx-cscx)?