Question

If cot theta =40/9 find cosec theta and sin theta

Answer 1

$\bold\pink{GivEn:-}$

$cot \theta = \dfrac{40}{9}$

$\bold\pink{To \ find:-}$

$cosec \theta = ? :\ and :\ sin \theta = ?$

$\bold\pink{Using \ identity:-}$

$cosec^2 \theta = 1 + cos^2 \theta$

$cosec^2 \theta = 1 + { \dfrac{40}{9}}^2$

$cosec^2 \theta = 1 + \dfrac{1600}{81}$

$cosec^2 \theta = \dfrac{81 + 1600}{81}$

$cosec^2 \theta = \dfrac{1681}{81}$

→ Taking square root both side :-

$\sqrt{cosec^2 \theta} = \sqrt{\dfrac{1681}{81}}$

$\sqrt{(Cosec)^2} = \sqrt{(\dfrac{41}{9})^2}$

$cosec\theta} = \dfrac{41}{9}}$

→ $sin \theta = \dfrac{1}{cosec \theta}$

$sin\theta} = \dfrac{9}{41}$

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