Question

Given : 4 sin^2 x = 1 find : x find : sin 2x find sin 3x

Answer 1

Answer :

★ x = 30°

★ sin 2x = 60°

★ sin 3x = 90°

Given :

• 4 sin²x = 1

To find :

The value of :-

• x
• sin 2x
• sin 3x

Solution :

$\longrightarrow \quad \sf {4 \sin}^{2}x = 1$

• Transposing 4 to the other side.

$\longrightarrow \quad \sf { \sin}^{2}x = \dfrac{1}{4}$

• Taking square root on ¼ and removing the square on sin²x.

$\longrightarrow \quad \sf \sin \: x = \sqrt\dfrac{1}{4}$

$\longrightarrow \quad \sf \sin \: x = \dfrac{1}{2}$

$\longrightarrow \quad \sf But \: \sin \: 30^{\circ} \: = \: \dfrac{1}{2}$

$\: \: \: \sf \sin \: x \: = \sin30^{ \circ}$

$\longrightarrow \quad \sf \not\sin \: x \: = \not\sin30^{ \circ}$

$\therefore \sf \purple{ x = 30^{ \circ}}$

The value of x = 30°.

→ sin 2x :-

$\longrightarrow \quad \sf \sin \: 2x$

$\longrightarrow \quad \sf \sin \: 2 \times 30^{ \circ}$

$\longrightarrow \quad \sf \red{ \sin2x = \: 60^{ \circ}}$

→ sin 3x :-

$\longrightarrow \quad \sf \sin 3x$

$\longrightarrow \quad \sf \sin 3 \times {30}^{ \circ}$

$\longrightarrow \quad \sf \sin {90}^{ \circ}$

$\longrightarrow \quad \sf \red{ \sin3x = \: 90^{ \circ}}$

⠀⠀⠀━━━━━━━━━━⠀⠀⠀

Know MorE :

$\Large{ \begin{tabular}{|c|c|c|c|c|c|} \cline{1-6} \theta & \sf 0^{\circ} & \sf 30^{\circ} & \sf 45^{\circ} & \sf 60^{\circ} & \sf 90^{\circ} \\ \cline{1-6} \sin & 0 & \dfrac{1}{2 } & \dfrac{1}{ \sqrt{2} } & \dfrac{ \sqrt{3}}{2} & 1 \\ \cline{1-6} \cos & 1 & \dfrac{ \sqrt{ 3 }}{2} } & \dfrac{1}{ \sqrt{2} } & \dfrac{ 1 }{ 2 } & 0 \\ \cline{1-6} \tan & 0 & \dfrac{1}{ \sqrt{3} } & 1 & \sqrt{3} & \infty \\ \cline{1-6} \cot & \infty & \sqrt{3} & 1 & \dfrac{1}{ \sqrt{3} } &0 \\ \cline{1 - 6} \sec & 1 & \dfrac{2}{ \sqrt{3}} & \sqrt{2} & 2 & \infty \\ \cline{1-6} \csc & \infty & 2 & \sqrt{2 } & \dfrac{ 2 }{ \sqrt{ 3 } } & 1 \\ \cline{1 - 6}\end{tabular}}$

Answer 2

$\Huge{\textbf{\textsf{{\color{blue}{ᗩи}}{\purple{ѕ}}{\red{ωєƦ}}{\color{yellow}{:}}}}}$

The required answers are : -

✮ x = 30°

✮ sin 2x = 60°

✮ sin 3x = 90°

➦Explanation is in the attachment.

✰✫✰✫✰✫✰✫✰✫✰✫

♬♫♪

➠Stay happy N Blessed