If sin 6- -sin 4- -sin 2- -0 then - is equal to n- z

The correct option is B nπ/4 or nπ±π/3 sin 6θ nbsp; +sin 2θ nbsp; +sin 4θ nbsp; =0 ⇒sin 6θ nbsp; +sin 2θ nbsp; = sin 4θ nbsp; ...

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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 $θ$ is equal to $(n ϵ z)$

\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}{6}

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Solution

The correct option is B $\frac{n π}{4}$ or $n π \pm \frac{π}{3}$
$sin 6 θ + sin 2 θ + sin 4 θ = 0 \Rightarrow sin 6 θ + sin 2 θ = - sin 4 θ \Rightarrow 2 sin 4 θ cos 2 θ = - sin 4 θ$
$sin 4 θ = 0 \Rightarrow 4 θ = n π ∴ θ = \frac{n π}{4}$
Or $cos 2 θ = \frac{- 1}{2} \Rightarrow 2 θ = 2 n π \pm \frac{2 π}{3} ∴ θ = n π \pm \frac{π}{3}$
Ans: A

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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. The range of

x

satisfying

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

and

| 2 sin x | < 1

is
(where

n \in Z

)

Q. If

| 2 sin θ - cosec θ | \geq 1

, then complete set of values of

θ

is
(where

n \in Z

)

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) $n π \pm π / 2$ $e) n π \pm π / 8$

sin [\frac{π}{4} cot θ] = cos [\frac{π}{4} tan θ]

, if

θ = n π - \frac{π}{4}, n \in I

. If true enter 1 else 0.

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If sin6θ+sin4θ+sin2θ=0 then θ is equal to (nϵz)

The correct option is B nπ4 or nπ±π3sin6θ+sin2θ+sin4θ=0⇒sin6θ+sin2θ=−sin4θ⇒2sin4θcos2θ=−sin4θsin4θ=0⇒4θ=nπ∴θ=nπ4Or cos2θ=−12⇒2θ=2nπ±2π3∴θ=nπ±π3Ans: A

If $sin 6 θ + sin 4 θ + sin 2 θ = 0$ then $θ$ is equal to $(n ϵ z)$