If cot $\theta = \frac{14}{3}$, then what is the value of cos $ \theta$ ? ($0^\circ < \theta < 90^\circ )$
If cot $\theta = \frac{14}{3}$, then what is the value of cos $ \theta$ ? ($0^\circ < \theta < 90^\circ )$
यदि cot $\theta = \frac{14}{3}$ है , तो cos $ \theta$ का मान ज्ञात कीजिए। ($0^\circ < \theta < 90^\circ )$
Detailed Solution & Logic
Correct Answer:
$\frac{14}{\sqrt{205}}$
$cot \theta = \frac{14}{3}$
$cot \theta = \frac{\text{Adjacent}}{\text{Opposite}}$
So,
Adjacent = 14, Opposite = 3
Hypotenuse $= \sqrt{14^2 + 3^2} = \sqrt{196 + 9} = \sqrt{205}$
Now,
$\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{14}{\sqrt{205}}$
Final Answer: $\frac{14}{\sqrt{205}}$
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