Question

if 17 cos A=8 find 15 cosec A -8 sec B​

Answer 1

cosA=8/17

then sin A = 15/17 (by Pythagoras

theorem)

cos B=15/17

15cosecA-8secB

15*1/sinA-8*1/cosB

15*17/15-8*17/8

17-17=0

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Answer 2

Answer:

$15 \csc A -8 \sec A=0$

Step-by-step explanation:

Given : $17\cos A=8$

To find : $15 \csc A -8 \sec A$

Solution :

$17\cos A=8$

$\cos A=\frac{8}{17}$

We know, $\sec A=\frac{1}{\cos A}$

$\sec A=\frac{1}{\frac{8}{17}}$

$\sec A=\frac{17}{8}$

We know, $\sin A=\sqrt{1-\cos^2 A}$

$\sin A=\sqrt{1-(\frac{8}{17})^2}$

$\sin A=\sqrt{\frac{17^2-8^2}{17^2}}$

$\sin A=\sqrt{\frac{225}{17^2}}$

$\sin A=\sqrt{(\frac{15}{17})^2}$

$\sin A=\frac{15}{17}$

$\csc A=\frac{1}{\sin A}$

$\csc A=\frac{1}{\frac{15}{17}}$

$\sec A=\frac{17}{15}$

Substitute in the expression,

$15 \csc A -8 \sec A=15\times\frac{17}{15}-8\times\frac{17}{8}$

$15 \csc A -8 \sec A=17-17$

$15 \csc A -8 \sec A=0$