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If #cos theta=21/29# determine #sec theta/ (tan theta- sin theta)#?

Answer 1

Grace Ashcraft

Given #cos theta=21/29#

To determine

#sec theta/ (tan theta- sin theta)#

#=(sec thetacostheta)/ (costheta*sintheta/costheta- costhetasin theta)#

#=1/ (sintheta- costhetasin theta)#

#=1/ (sintheta(1- costheta))#

#=1/ (sqrt(1-cos^2theta)(1- costheta))#

#=1/ (sqrt(1-21^2/29^2)(1- 21/29))#

#=29^2/ (sqrt(29^2-21^2)(29- 21))#

#=29^2/ (20*8)=841/160#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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