the quadrantic equation whose roots are sin2 18 ,cos2 36
Answers
Answer:
Step-by-step explanation:
ANSWER
(A) Sum of the roots
=sin
2
18
∘
+cos
2
36
∘
=[
4
5
−1
]
2
+[
4
5
+1
]
2
=
16
1
[(
5
+1)
2
+(
5
−1)
2
]
=(
16
1
)[2(5+1)]=
4
3
Product of the roots
=sin
2
18
∘
.cos
2
36
∘
=[
4
5
−1
]
2
.[
4
5
+1
]
2
=[
4.4
5−4
]
2
=
16
1
∴ Quadratic Equation is
x
2
−[sin
2
18
∘
+cos
2
36
∘
]x+(sin
2
18
∘
cos
2
36
∘
)
⇒x
2
−(3/4)x+(1/16)=0
⇒16x
2
−12x+1=0
Answered ByANSWER
(A) Sum of the roots
=sin
2
18
∘
+cos
2
36
∘
=[
4
5
−1
]
2
+[
4
5
+1
]
2
=
16
1
[(
5
+1)
2
+(
5
−1)
2
]
=(
16
1
)[2(5+1)]=
4
3
Product of the roots
=sin
2
18
∘
.cos
2
36
∘
=[
4
5
−1
]
2
.[
4
5
+1
]
2
=[
4.4
5−4
]
2
=
16
1
∴ Quadratic Equation is
x
2
−[sin
2
18
∘
+cos
2
36
∘
]x+(sin
2
18
∘
cos
2
36
∘
)
⇒x
2
−(3/4)x+(1/16)=0
⇒16x
2
−12x+1=0
Answered ByANSWER
(A) Sum of the roots
=sin
2
18
∘
+cos
2
36
∘
=[
4
5
−1
]
2
+[
4
5
+1
]
2
=
16
1
[(
5
+1)
2
+(
5
−1)
2
]
=(
16
1
)[2(5+1)]=
4
3
Product of the roots
=sin
2
18
∘
.cos
2
36
∘
=[
4
5
−1
]
2
.[
4
5
+1
]
2
=[
4.4
5−4
]
2
=
16
1
∴ Quadratic Equation is
x
2
−[sin
2
18
∘
+cos
2
36
∘
]x+(sin
2
18
∘
cos
2
36
∘
)
⇒x
2
−(3/4)x+(1/16)=0
⇒16x
2
−12x+1=0
Answered ByANSWER
(A) Sum of the roots
=sin
2
18
∘
+cos
2
36
∘
=[
4
5
−1
]
2
+[
4
5
+1
]
2
=
16
1
[(
5
+1)
2
+(
5
−1)
2
]
=(
16
1
)[2(5+1)]=
4
3
Product of the roots
=sin
2
18
∘
.cos
2
36
∘
=[
4
5
−1
]
2
.[
4
5
+1
]
2
=[
4.4
5−4
]
2
=
16
1
∴ Quadratic Equation is
x
2
−[sin
2
18
∘
+cos
2
36
∘
]x+(sin
2
18
∘
cos
2
36
∘
)
⇒x
2
−(3/4)x+(1/16)=0
⇒16x
2
−12x+1=0
Answered ByANSWER
(A) Sum of the roots
=sin
2
18
∘
+cos
2
36
∘
=[
4
5
−1
]
2
+[
4
5
+1
]
2
=
16
1
[(
5
+1)
2
+(
5
−1)
2
]
=(
16
1
)[2(5+1)]=
4
3
Product of the roots
=sin
2
18
∘
.cos
2
36
∘
=[
4
5
−1
]
2
.[
4
5
+1
]
2
=[
4.4
5−4
]
2
=
16
1
∴ Quadratic Equation is
x
2
−[sin
2
18
∘
+cos
2
36
∘
]x+(sin
2
18
∘
cos
2
36
∘
)
⇒x
2
−(3/4)x+(1/16)=0
⇒16x
2
−12x+1=0
Answered By