Question

if x cos a=8 and 15cosec a=8sec a then the value of x is
a) 20 b)16 c)17 d)13​

Answer 1

Answer:

CosA=8/17

Third side=√17^2–8^2=√289–64=√225=15

CosecA=17/15

15cosec A=15×17/15=17

SecB=17/15

8 secB=8×17/15=126/15

17–126/15=(255–126)/15=12915

Answer 2

SOLUTION

GIVEN

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

TO CHOOSE THE CORRECT OPTION

The value of x

a) 20

b) 16

c) 17

d) 13

EVALUATION

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

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

Again

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

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

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

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

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

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

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

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

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

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

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

$\displaystyle\sf \implies x = 17$

So the value of x = 17

FINAL ANSWER

Hence the the option is c) 17

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