Question

find the value oh theta if 2sin2theta is equal to root3​

Answer 1

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✯ Correct question :-

Find the value of θ if 2sin[ 2θ ] = √3

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✯ Solution :-

2sin²θ = √3

Simplifying ,

⇒ sin2θ = √3/2

As we know that , sin60° = √3

By comparing ,

⇒ sin2θ = sin60°

⇒ 2θ = 60°

⇒ θ = 60°/2

⇒ θ = 30°

Hence , θ = 30°

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✯ More information :-

Trigonometric identities

• sin²A + cos²A = 1
• sec²A - tan²A = 1
• cosec²A - cot²A = 1

Trigonometric ratios values of angles

θ = 0° , 30° , 45° , 60° , 90°

Ratios

◉ sinθ =

• 0° → 0
• 30° → 1/2
• 45° → 1/√2
• 60° → √3/2
• 90° → 1

◉ cosθ

• 0° → 1
• 30° → √3/2
• 45° → 1/√2
• 60° → √3/2
• 90° → 0

◉ tanθ

• 0° → 0
• 30° → 1/√3
• 45° → 1
• 60° → √3
• 90° → ∞

◉ cosecθ

• 0° → ∞
• 30° → 2
• 45° → √2
• 60° → 2/√3
• 90° → 1

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Answer 2

Answer:

θ = 30°

Step-by-step explanation:

$\large \tt 2(sin2 \theta) = \sqrt{3} \implies sin2 \theta \: = \frac{ \sqrt{3} }{2}$

$\large \tt we \: \: know \: \: that \: \leadsto \: \: sin60\degree \: = \frac{ \sqrt{3} }{2}$

then ,

$\tt \cancel{sin} \: 2 \theta \: = \cancel{ sin} \: 60 \degree \: \: \implies \: \: 2 \theta \: = 60 \degree$

$\huge \tt \ast \: the \: value \: of \: \theta \: = 30 \degree$