what will be the value of expression when theta lies between π/2 and π
Answers
Answer:
1+sin
2
θ
sin
2
θ
sin
2
θ
cos
2
θ
1+cos
2
θ
cos
2
θ
4sin4θ
4sin4θ
1+4sin4θ
∣
∣
∣
∣
∣
∣
∣
∣
C
1
→C
1
+C
2
∣
∣
∣
∣
∣
∣
∣
∣
1+sin
2
θ+cos
2
θ
sin
2
θ+cos
2
θ+1
sin
2
θ+cos
2
θ
cos
2
θ
1+cos
2
θ
cos
2
θ
4sin4θ
4sin4θ
1+4sin4θ
∣
∣
∣
∣
∣
∣
∣
∣
=0
⇒
∣
∣
∣
∣
∣
∣
∣
∣
1+1
1+1
1
cos
2
θ
1+cos
2
θ
cos
2
θ
4sin4θ
4sin4θ
1+4sin4θ
∣
∣
∣
∣
∣
∣
∣
∣
⇒
∣
∣
∣
∣
∣
∣
∣
∣
2
2
1
cos
2
θ
1+cos
2
θ
cos
2
θ
4sin4θ
4sin4θ
1+4sin4θ
∣
∣
∣
∣
∣
∣
∣
∣
R
2
:R
2
→R
2
−R
1
R
3
→R
3
−R
1
⇒
∣
∣
∣
∣
∣
∣
∣
∣
2
2−2
2−2
cos
2
θ
1+cos
2
θ−cos
2
θ
cos
2
θ−cos
2
θ
4sin4θ
4sin4θ−4sin4θ
1+4sin4θ−4sin4θ
∣
∣
∣
∣
∣
∣
∣
∣
=0
∣
∣
∣
∣
∣
∣
∣
∣
2
0
−1
cos
2
θ
1
0
4sin4θ
0
1
∣
∣
∣
∣
∣
∣
∣
∣
=0
Expand
⇒0+(1)[2−(−1)(4sin4θ)]=0
⇒2+4sin4θ=0
⇒sin4θ=
4
−2
⇒sin4θ=
2
−1
⇒4θ=π+
6
π
,4θ=2π−
6
π
[∵ only in 3
rd
and 4
th
quadrants sin is negative]
⇒4θ=
6
7π
,
6
11π
θ=
24
7π
,
24
11π
Answer:
2+sin
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