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1

1

$begingroup$

Let $a$ be a real positive number.

(I) $quad a> fracsin(y_1(a))y_1(a)$ where $y_1(a)$ is the unique root of $y=a cot(y)$ in $(0,fracpi2)$.

(II) $quad a>xi$ where $xi$ is the unique root of $xi^2=cos(xi)$ in $(0,fracpi2)$.

I have read that the two statements are equivalent, i.e. (I)$iff$(II).
Does anyone have any hint how to prove this equivalence?

trigonometry inequality equivalence-relations

share|cite|improve this question

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112

$endgroup$

add a comment | 

1

1

$begingroup$

Let $a$ be a real positive number.

(I) $quad a> fracsin(y_1(a))y_1(a)$ where $y_1(a)$ is the unique root of $y=a cot(y)$ in $(0,fracpi2)$.

(II) $quad a>xi$ where $xi$ is the unique root of $xi^2=cos(xi)$ in $(0,fracpi2)$.

I have read that the two statements are equivalent, i.e. (I)$iff$(II).
Does anyone have any hint how to prove this equivalence?

trigonometry inequality equivalence-relations

share|cite|improve this question

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112

$endgroup$

add a comment | 

$begingroup$

Let $a$ be a real positive number.

(I) $quad a> fracsin(y_1(a))y_1(a)$ where $y_1(a)$ is the unique root of $y=a cot(y)$ in $(0,fracpi2)$.

(II) $quad a>xi$ where $xi$ is the unique root of $xi^2=cos(xi)$ in $(0,fracpi2)$.

I have read that the two statements are equivalent, i.e. (I)$iff$(II).
Does anyone have any hint how to prove this equivalence?

trigonometry inequality equivalence-relations

share|cite|improve this question

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112

$endgroup$

share|cite|improve this question

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112

share|cite|improve this question

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112

asked Mar 29 at 11:11

William TomblinWilliam Tomblin

261112