Solve sin- -sin 5- -sin 3- 0-

On simplification, sin 3θ (2cos 2θ +1)=0 ∴θ =nπ /3, θ =nπ±π/3 for given range θ =0, π/3 ∴θ =0, π/3 . ...

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Standard XII

Mathematics

Principal Solution of Trigonometric Equation

Solve sinθ ...

Question

Solve $sin θ + sin 5 θ = sin 3 θ; 0 \leq θ \leq π$ .

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Solution

On simplification, $sin 3 θ (2 cos 2 θ + 1) = 0$
$∴ θ = n π / 3, θ = n π \pm π / 3$ for given range $θ = 0, π / 3$ $∴ θ = 0, π / 3$ .

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Similar questions

Q. Solve:

sin 5 θ + sin θ = sin 3 θ

Q. Find all the values of

θ

satisfying the equation :

sin θ + sin 5 θ = sin 3 θ

such that

0 \leq θ \leq π

Q. Find the number of roots of the equation

sin θ + sin 5 θ = sin 3 θ

[0, π]

$Solve the following equations : (i) c o s θ + c p s 2 θ + c o s 3 θ = 0 (i i) c o s θ + c o s 3 θ - c o s 2 θ = 0 (i i i) s i n θ + s i n 5 θ = s i n 3 θ (i v) c o s θ c o s 2 θ c o s 3 θ = \frac{1}{4} (v) c o s θ + s i n θ = c o s 2 θ + s i n 2 θ (v i) s i n θ + s i n 2 θ + s i n 3 θ = 0 (v i i) s i n θ + s i n 2 θ + s i n 3 θ + s i n 4 θ = 0 (v i i i) s i n 3 θ - s i n θ = 4 c o s^{2} θ - 2 (i x) s i n 2 θ - s i n 4 θ + s i n 6 θ = 0$

\frac{sin 3 θ + 2 sin 5 θ + sin 7 θ}{sin θ + 2 sin 3 θ + sin 5 θ} = cos 2 θ + sin 2 θ . cot 3 θ

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Solve sinθ+sin5θ=sin3θ;0≤θ≤π.

On simplification, sin3θ(2cos2θ+1)=0∴θ=nπ/3,θ=nπ±π/3 for given range θ=0,π/3 ∴θ=0,π/3.

Solve $sin θ + sin 5 θ = sin 3 θ; 0 \leq θ \leq π$ .

On simplification, $sin 3 θ (2 cos 2 θ + 1) = 0$
$∴ θ = n π / 3, θ = n π \pm π / 3$ for given range $θ = 0, π / 3$ $∴ θ = 0, π / 3$ .