10 If 17 cos A = 8, find 15 cosec A - 8 sec B.
Answers
Answer:
Given : 17\cos A=817cosA=8
To find : 15 \csc A -8 \sec A15cscA−8secA
Solution :
17\cos A=817cosA=8
\cos A=\frac{8}{17}cosA=
17
8
We know, \sec A=\frac{1}{\cos A}secA=
cosA
1
\sec A=\frac{1}{\frac{8}{17}}secA=
17
8
1
\sec A=\frac{17}{8}secA=
8
17
We know, \sin A=\sqrt{1-\cos^2 A}sinA=
1−cos
2
A
\sin A=\sqrt{1-(\frac{8}{17})^2}sinA=
1−(
17
8
)
2
\sin A=\sqrt{\frac{17^2-8^2}{17^2}}sinA=
17
2
17
2
−8
2
\sin A=\sqrt{\frac{225}{17^2}}sinA=
17
2
225
\sin A=\sqrt{(\frac{15}{17})^2}sinA=
(
17
15
)
2
\sin A=\frac{15}{17}sinA=
17
15
\csc A=\frac{1}{\sin A}cscA=
sinA
1
\csc A=\frac{1}{\frac{15}{17}}cscA=
17
15
1
\sec A=\frac{17}{15}secA=
15
17
Substitute in the expression,
15 \csc A -8 \sec A=15\times\frac{17}{15}-8\times\frac{17}{8}15cscA−8secA=15×
15
17
−8×
8
17
15 \csc A -8 \sec A=17-1715cscA−8secA=17−17
15 \csc A -8 \sec A=015cscA−8secA=0