How do you simplify $cot θ sec θ sin θ$ $cot theta sec theta sin theta$ ?

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Answer 1 · 2018-03-25T07:12:43

The expression is equal to $1$ $1$ .

Use these two identities:

$cot θ = \frac{1}{tan θ} = \frac{1}{\frac{sin θ}{cos θ}} = \frac{cos θ}{sin θ}$ $cottheta=1/tantheta=1/(sintheta/costheta)=costheta/sintheta$

$sec θ = \frac{1}{cos θ}$ $sectheta=1/costheta$

Here's the expression:

$= cot θ sec θ sin θ$ $color(white)=cotthetasecthetasintheta$

$= cot θ \cdot sec θ \cdot sin θ$ $=cottheta*sectheta*sintheta$

$= \frac{cos θ}{sin θ} \cdot \frac{1}{cos θ} \cdot sin θ$ $=costheta/sintheta*1/costheta*sintheta$

$=color(red)cancelcolor(black)costheta/sintheta*1/color(red)cancelcolor(black)costheta*sintheta$

$=1/sintheta*1*sintheta$

$=1/sintheta*sintheta$

$=1/color(red)cancelcolor(black)sintheta*color(red)cancelcolor(black)sintheta$

$=1$

That's it. Hope this helped!

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