Question

X cosA=8 15cosecA=8secA then find value of X?​

Answer 1

Answer:

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Answer 2

SOLUTION

GIVEN

$\displaystyle\sf x \cos A = 8 \: \: and \: \: 15 cosec A = 8 \sec A$

TO DETERMINE

The value of x

EVALUATION

$\displaystyle\sf x \cos A = 8 \: \: \: \:$

$\displaystyle\sf \cos A = \frac{8}{x} \: \: \: \: - - - - (1)$

Again

$\displaystyle\sf 15 cosec A = 8 \sec A$

$\displaystyle\sf \implies \: \frac{15}{ \sin A} = \frac{8}{ \cos A}$

$\displaystyle\sf \implies \: \frac{\sin A}{ \cos A} = \frac{15}{8}$

$\displaystyle\sf \implies \: \tan A = \frac{15}{8}$

$\displaystyle\sf \implies {\tan}^{2} A = \frac{225}{64}$

$\displaystyle\sf \implies 1 + {\tan}^{2} A = 1 + \frac{225}{64}$

$\displaystyle\sf \implies {\sec}^{2} A = \frac{64 + 225}{64}$

$\displaystyle\sf \implies {\sec}^{2} A = \frac{289}{64}$

$\displaystyle\sf \implies \sec A = \frac{17}{8}$

$\displaystyle\sf \implies \cos A = \frac{8}{17}$

$\displaystyle\sf \implies \frac{8}{x }= \frac{8}{17}$

$\displaystyle\sf \implies x = 17$

FINAL ANSWER

Hence the required value of x = 17

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