Solving \(\displaystyle{\cos{{\left({{\tan}^{{-{1}}}{x}}\right)}}}={\sin{{\left({{\cot}^{{-{1}}}{\frac{{{3}}}{{{4}}}}}\right)}}}\)

Dexter Odom

Dexter Odom

Answered question

2022-04-01

Solving cos(tan1x)=sin(cot134)

Answer & Explanation

Boehm98wy

Boehm98wy

Beginner2022-04-02Added 18 answers

Well, we can use that:
cos(arctan(x))=11+x2
And
sin(arccot(x))=1x1+1x2
So in your case, we need to solve:
11+x2=1341+1(34)2=45x=±34
zevillageobau

zevillageobau

Beginner2022-04-03Added 13 answers

cos(arctanx)=cos(arctan34)
arctanx=2mπ±arctan34=2mπ+arctan(±34)
where m is any integer as arctan(a)=arctan(a)
As π2<arctanyπ2
arctanx=arctan(±34)
Apply tan on both sides

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