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P-2 Trigonometry — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsP-2 Trigonometry3 Marks
Question
If $\cot \theta=\frac{40}{9},$ find the values of cosecθ and sinθ.
✓

Answer

We know that,
$\operatorname{cosec}^2 \theta=1+\cot ^2 \theta$
$\Rightarrow \operatorname{cosec}^2 \theta=1+\left(\frac{40}{9}\right)^2$
$\Rightarrow \operatorname{cosec}^2 \theta=1+\frac{1600}{81}$
$\Rightarrow \operatorname{cosec}^2 \theta=\frac{1681}{81}$
$\Rightarrow \operatorname{Cosec} \theta=\frac{41}{9}$
$\Rightarrow$ Also,
$\Rightarrow \sin \theta=\frac{1}{\operatorname{cosec} \theta}$
$\therefore \sin \Theta=\frac{9}{41}$
 

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