If $ \frac{x}{y} = cot \theta $, where $\theta $ is an acute angle, then $ cosec \theta $ = _________.
If $ \frac{x}{y} = cot \theta $, where $\theta $ is an acute angle, then $ cosec \theta $ = _________.
यदि $ \frac{x}{y} = cot \theta $, जहां $\theta $ एक न्यून कोण है, तो $ cosec \theta $ का मान ज्ञात कीजिए। = _________.
Detailed Solution & Logic
Correct Answer:
$\frac{\sqrt{x^2 + y^2}} {y}$
Solution:
Given:
$ \frac{x}{y} = \cot \theta $
We know:
$ \cot \theta = \frac{\text{base}}{\text{perpendicular}} $
So,
Base = x, Perpendicular = y
Hypotenuse:
$ = \sqrt{x^2 + y^2} $
Now,
$ \csc \theta = \frac{\text{hypotenuse}}{\text{perpendicular}} $
$ = \frac{\sqrt{x^2 + y^2}}{y} $
Final Answer:
$ \frac{\sqrt{x^2 + y^2}}{y} $
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