1
17. If 2 sin 0 = x +1/x
prove that sin 3 theta + 1/2( x^3 + x^3) = 0
Answers
Step-by-step explanation:
ldmskdkdkdkdkkdkdlxlxlx727778f.v,vm,hi[fjidofujid a day of a day of a day of a day of a day of a day of a 77kdkdlflfldld
Answer:
✪ᴀɴsᴡᴇʀ✪
☆ɢɪᴠᴇɴ☆
2sin(\theta) = x + \frac{1}{x} 2sin(θ)=x+
x
1
☆ᴛᴏ ᴘʀᴏᴠᴇ☆
sin(3\theta) + \frac{1}{2}(x^3 + \frac{1}{x^3}) = 0sin(3θ)+
2
1
(x
3
+
x
3
1
)=0
☆ᴘʀᴏᴏғ☆
\:\:\:\:sin(3\theta)sin(3θ)
= 3sin(\theta) -4sin^3(\theta) =3sin(θ)−4sin
3
(θ)
= \frac{3}{2}(x + \frac{1}{x}) -4[\frac{1}{2}(x + \frac{1}{x})]^3=
2
3
(x+
x
1
)−4[
2
1
(x+
x
1
)]
3
= \frac{3}{2}(x + \frac{1}{x}) -\frac{4}{8}(x + \frac{1}{x})^3=
2
3
(x+
x
1
)−
8
4
(x+
x
1
)
3
= \frac{3}{2}(x + \frac{1}{x})=
2
3
(x+
x
1
)
\:\:\:\: -\frac{1}{2}[x^3 + \frac{1}{x^3} + 3x.\frac{1}{x}(x + \frac{1}{x})]−
2
1
[x
3
+
x
3
1
+3x.
x
1
(x+
x
1
)]
= \frac{3}{2}(x + \frac{1}{x})-\frac{1}{2}(x^3 + \frac{1}{x^3}) -\frac{3}{2}(x + \frac{1}{x})=
2
3
(x+
x
1
)−
2
1
(x
3
+
x
3
1
)−
2
3
(x+
x
1
)
\implies sin(3\theta) = -\frac{1}{2}(x^3 + \frac{1}{x^3})⟹sin(3θ)=−
2
1
(x
3
+
x
3
1
)
\implies sin(3\theta) + \frac{1}{2}(x^3 + \frac{1}{x^3}) = 0⟹sin(3θ)+
2
1
(x
3
+
x
3
1
)=0
Hence Proved
Step-by-step explanation:
mark has brainlest like hope it will help u