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Joint Entrance Examination
Mathematics
Trigonometric Ratios and Identities
Question 16
Question 16 of 298
Easy
MCQ
If
sin
x
=
−
3
5
\sin x=-\frac{3}{5}
sin
x
=
−
5
3
, where
π
<
x
<
3
π
2
\pi <x<\frac{3\pi }{2}
π
<
x
<
2
3
π
, then
80
(
tan
2
x
−
cos
x
)
80({\tan }^{2}x-\cos x)
80
(
tan
2
x
−
cos
x
)
is equal to
A
109
B
108
C
19
D
18
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Solutions · 1
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Official solution
sin
x
=
−
3
5
π
<
x
<
3
π
2
tan
x
=
3
4
,
cos
x
=
−
4
5
∴
80
(
tan
2
x
−
cos
x
)
=
80
(
9
16
+
4
5
)
=
80
(
45
+
64
80
)
=
109
\begin{gathered} \sin x=-\frac{3}{5}\pi <x<\frac{3\pi }{2} \\ \, \tan x=\frac{3}{4},\cos x=\frac{-4}{5} \\ \therefore 80({\tan }^{2}x-\cos x) \\ =80(\frac{9}{16}+\frac{4}{5}) \\ =80(\frac{45+64}{80}) \\ =109 \end{gathered}
sin
x
=
−
5
3
π
<
x
<
2
3
π
tan
x
=
4
3
,
cos
x
=
5
−
4
∴
80
(
tan
2
x
−
cos
x
)
=
80
(
16
9
+
5
4
)
=
80
(
80
45
+
64
)
=
109
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