How do you simplify #cot theta sec theta sin theta#?

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Answer 1 · 2018-03-25T07:12:43

The expression is equal to #1#.

Use these two identities:

#cottheta=1/tantheta=1/(sintheta/costheta)=costheta/sintheta#

#sectheta=1/costheta#

Here's the expression:

#color(white)=cotthetasecthetasintheta#

#=cottheta*sectheta*sintheta#

#=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!