Simplify $cot x (sec x + tan x)$ $cotx(secx+tanx)$ ?

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Answer 1 · 2017-05-01T16:18:05

Please see below.

$cot x (sec x + tan x)$ $cotx(secx+tanx)$

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

= $\frac{cos x}{sin x} \times \frac{1}{cos x} + \frac{cos x}{sin x} \times \frac{sin x}{cos x}$ $cosx/sinx xx 1/cosx+cosx/sinx xx sinx/cosx$

= $cancelcosx/sinx xx 1/cancelcosx+cancelcosx/cancelsinx xx cancelsinx/cancelcosx$

= $1/sinx+1$

= $cscx+1$

Simplify cotx(secx+tanx)cotx(secx+tanx)cotx(secx+tanx)?