Question

If x cos a=8 and 15 cosec a=8 sec a, then the value of x is

Answer 1

Answer:

Hence the value of x is 17

Answer 2

$x = \frac{64}{17}$

Explanation:

$Given, \: \: 15cosec \: a = 8sec \: a \\ or, \: \: \frac{15}{sin \: a} = \frac{8}{cos \: a} \\ or, \: \: \frac{sin \: a}{cos \: a} = \frac{15}{8} \\ or, \: \: tan \: a = \frac{15}{8} \\ we \: \: know \: \: \boxed{ \: \: sec \: a = \sqrt{1 + tan^{2} a} } \\ then, \: \: sec \: a = \sqrt{1 + {( \frac{15}{8} })^{2} } = \sqrt{\frac{289}{64} } = \frac{17}{8} \\ Now, \: \: x = 8cos \: a = \frac{8}{sec \: a} \\ x = \frac{8}{ \frac{17}{8} } = 8 \times \frac{8}{17} \\ x = \frac{64}{17}$