If sin 6- -sin 4- -sin 2- -0- then general value of - is

The correct option is A nπ 4 ,nπ±π 3 #160; sin 6θ #160; +sin 4θ #160; +sin 2θ #160; =0 sin 4θ #160; +2sin 4θ #160; sin 2θ #16 ...

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Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

If sin 6θ +...

Question

If $sin 6 θ + sin 4 θ + sin 2 θ = 0$ , then general value of $θ$ is

\frac{n π}{4}, n π \pm \frac{π}{3}

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\frac{n π}{4}, n π \pm \frac{π}{6}

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\frac{n π}{4}, 2 n π \pm \frac{π}{3}

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\frac{n π}{4}, 2 n π \pm \frac{π}{6}

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Solution

The correct option is A $\frac{n π}{4}, n π \pm \frac{π}{3}$
$sin 6 θ + sin 4 θ + sin 2 θ = 0$

$sin 4 θ + 2 sin 4 θ sin 2 θ = 0$

$sin 4 θ (1 + 2 cos 2 θ) = 0$

$sin 4 θ = 0 o r cos 2 θ = - \frac{1}{2} = cos \frac{2 π}{3}$

$4 θ = n π o r 2 θ = 2 n π \pm \frac{2 π}{3}$

$θ = \frac{n π}{4} o r θ = n π \pm \frac{π}{3}$

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Similar questions

Solve the equation: $\sqrt{(\frac{1}{16} + c o s^{4} x - \frac{1}{2} c o s^{2} x)} + \sqrt{(\frac{9}{16} + c o s^{4} x - \frac{3}{2} c o s^{2} x)} = \frac{1}{2}$

Q. If

| 2 sin θ - cosec θ | \geq 1

, then complete set of values of

θ

is
(where

n \in Z

)

Q. The range of

x

satisfying

tan x - {tan}^{2} x > 0

and

| 2 sin x | < 1

is
(where

n \in Z

)

$The general value of x satisfying the equation \sqrt{3} s i n x + c o s x = \sqrt{3} i s g i v e n b y$

List-I	List-II
$1) {tan}^{2} θ = 1$	a $) n π \pm π / 6$
$2) {cos}^{2} θ = \frac{1}{4}$	b $) n π \pm π / 4$
$3) {sin}^{2} θ = \frac{1}{4}$	c $) n π \pm π / 3$
4) cosec $θ = 1$	d) $n π \pm π / 2$ $e) n π \pm π / 8$

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If sin6θ+sin4θ+sin2θ=0, then general value of θ is

The correct option is A nπ4,nπ±π3 sin6θ+sin4θ+sin2θ=0sin4θ+2sin4θsin2θ=0sin4θ(1+2cos2θ)=0sin4θ=0orcos2θ=−12=cos2π34θ=nπor2θ=2nπ±2π3θ=nπ4orθ=nπ±π3

If $sin 6 θ + sin 4 θ + sin 2 θ = 0$ , then general value of $θ$ is