V2 Sin 0. If tan x = 4/3, then find the value of tan x/2 (1/2)
Answers
Answer: ∴tan
2
x
=2
Step-by-step explanation: As tanx=−
3
4
,
2
π
<x<π
i.e x lies in 2nd quadrant
Hence tanx=−
3
4
⇒sinx=
4
2
+3
2
4
=
5
4
And cosx=−
4
2
+3
2
5
=−
5
3
Now using 1−cosx=2sin
2
2
x
⇒sin
2
x
=±
2
1−cosx
, we get
sin
2
x
=±
2
1−(−
5
3
)
=±
10
8
As
2
π
<x<π⇒
4
π
<
2
x
<
2
π
and sine is positive in 1st quadrant
Then sin
2
x
=
5
2
Using 1+cosx=2cos
2
2
x
⇒cos
2
x
=±
2
1+cosx
We get, cos
2
x
=±
2
1+(−
5
3
)
=±
10
2
2
π
<x<π⇒
4
π
<
2
x
<
2
π
and cos is positive 1st quadrant
∴cos
2
x
=
5
1
Using cosx=
1+tan
2
2
x
1−tan
2
2
x
⇒tan
2
x
=±
1+cosx
1−cosx
We get, tan
2
x
=±
1+(−
5
3
)
1−(−
5
3
)
=±
4
As
2
π
<x<π⇒
4
π
<
2
x
<
2
π
and tan is positive in 1st quadrant
∴tan
2
x
=2