Question

If cosec theta is equal to 5 by 4 cot theta find the value of cot theta

Answer 1

Answer:

$cosec \alpha = \frac{5}{4} cot \alpha \\ \frac{1}{sin \alpha } = \frac{5 \: cos \alpha }{4 \: sin \alpha } \\ 5 \: cos \alpha = 4 \\ cos \alpha = \frac{4}{5} \\ sin \alpha = \sqrt{1 - {( \frac{4}{5} )}^{2} } = \sqrt{ \frac{25 - 16}{25} } = \frac{3}{5} \\ so \: cot \alpha = \frac{cos \alpha }{sin \alpha } = \frac{4}{3} \: ans.$