If sin6-sin4-sin2-0- then the general value of - is

The correct option is A nπ4, nπ±π3 sin 6θ+sin 4θ+sin 2θ=0 ⇒ sin 6θ+sin 2θ+sin 4θ=0 ⇒ 2sin6θ+2θ2cos6θ 2θ2+sin 4θ=0 ⇒ 2 sin 4θ cos 2θ+si ...

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Standard XII

Mathematics

General Solution of Trigonometric Equation

If sin6θ+si...

Question

If $s i n 6 θ + s i n 4 θ + s i n 2 θ = 0$ , then the 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 $\frac{n π}{4}, n π \pm \frac{π}{3}$
$s i n 6 θ + s i n 4 θ + s i n 2 θ = 0$
$\Rightarrow s i n 6 θ + s i n 2 θ + s i n 4 θ = 0$
$\Rightarrow 2 s i n \frac{6 θ + 2 θ}{2} c o s \frac{6 θ - 2 θ}{2} + s i n 4 θ = 0$
$\Rightarrow 2 s i n 4 θ c o s 2 θ + s i n 4 θ = 0$
$\Rightarrow s i n 4 θ [2 c o s 2 θ + 1] = 0$
$\Rightarrow s i n 4 θ = 0$
or $2 c o s 2 θ + 1 = 0$
$2 c o s 2 θ = - 1$
$4 θ = n π c o s 2 θ = \frac{- 1}{2} = c o s \frac{2 π}{3}$
$θ = \frac{n π}{4} 2 θ = 2 n π \pm \frac{2 π}{3}$
$\Rightarrow θ = n π \pm \frac{π}{3}$

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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 the general value of θ is

The correct option is A nπ4,nπ±π3sin6θ+sin4θ+sin2θ=0⇒sin6θ+sin2θ+sin4θ=0⇒2sin6θ+2θ2cos6θ−2θ2+sin4θ=0⇒2sin4θcos2θ+sin4θ=0⇒sin4θ[2cos2θ+1]=0⇒sin4θ=0or 2cos2θ+1=02cos2θ=−14θ=nπcos2θ=−12=cos2π3θ=nπ42θ=2nπ±2π3⇒θ=nπ±π3

If $s i n 6 θ + s i n 4 θ + s i n 2 θ = 0$ , then the general value of $θ$ is