If cot theta=9/40 pi greater than theta greater than 3pi/2,find the values of cosec theta , tan theta, sec theta , cos theta, sin theta
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ANSWER
tanx=
4
3
π<x<3
2
π
180<x<
2
3
×180
=180<x<270
=90<
2
x
<
2
270
=
2
π
<
2
x
<
4
3π
⇒
2
x
lies in 2
nd
quadrant.
sin
2
x
is positive.
cos
2
x
is negative.
tan
2
x
is negative.
tanx=
4
3
tanx=
1−tan
2
2
x
2tan
2
x
=
4
3
=
1−tan
2
2
x
2tan
2
x
⇒3−3tan
2
2
x
=8tan
2
x
⇒3tan
2
2
x
+8tan
2
x
−3=0
⇒3tan
2
2
x
+9tan
2
x
−tan
2
x
−3=0
⇒3tan
2
x
(tan
2
x
+3)−1(tan
2
x
+3)=0
3tan
2
x
−1=0 & tan
2
x
+3=0
⇒3tan
2
x
=1 tan
2
x
=−3
⇒tan
2
x
=
3
1
(not possible as tan
2
x
is negative}
∴tan
2
x
=−3
Consider, cos
2
x
=
sec
2
x
1
=
1+tan
2
2
x
−1
=
1+(−3)
2
−1
=
10
−1
∴cos
2
x
=
10
−1
Consider,
sin
2
x
=tan
2
x
×cos
2
x
=(−3)(−1/
10
)
=
10
3
.
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