I have the below question and have to

Tony Mccarthy

Tony Mccarthy

Answered question

2022-03-30

I have the below question and have to find value of x.
cos1(x21x2+1)+tan1(2xx21)=2π3

Answer & Explanation

Nyla Trujillo

Nyla Trujillo

Beginner2022-03-31Added 9 answers

let x=cott=costsint, then
x21x2+1=cos2tsin2t1cos2tsin2t+1=cos(2t),
2xx21=2costsintcos2tsin2t1=tan2t
now we have
2π3=cos1(cos(2t))+tan1(tan2t)
=(2t+2kπ)+(2t+mπ)
=(2t)+(2t),(2t)+(2tπ)
=4t,4tπ,
therefore we get
t=π6,5π12,
x=3,23

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