Prove the following are identities using the definitions of the inverse trig functions and show all steps. Assume the relevant part of the cofunction theorem for part b, that is cot(theta)=tan(pi/2 - theta) for all angles theta with theta cannot equal npi for each integer n. b:cot^-1x= pi/2- tan^-1 x

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Asked Oct 1, 2019
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Prove the following are identities using the definitions of the inverse trig functions and show all steps. Assume the relevant part of the cofunction theorem for part b, that is cot(theta)=tan(pi/2 - theta) for all angles theta with theta cannot equal npi for each integer n.

 

b:cot^-1x= pi/2- tan^-1 x

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Expert Answer

Step 1

According to the given information it is needed to prove that:

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tanx 2 cot

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Step 2

Let us assume that;

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cot xe xcot e л by given condition that is cot0=tan| xtan 2 -1 ө tan xX=_- 2

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Step 3

Now, substitute the value of theta...

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tan 2 put 6-cotx cotx 2 tan x -1 tan -1 x cot x 2

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