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If sin 2θ = √3/2 then the value of sin 3θ is equal to: (take (0° ≤ θ ≤ 90°) (SSC CHSL 2015)
- a)0
- b)√3/2
- c)1
- d)1/2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If sin 2θ = √3/2 then the value of sin 3θ is equal t...
Given Information:
sin 2θ = √3/2
To find:
sin 3θ
Solution:
Using Trigonometric Identity:
sin 3θ = 3sin θ - 4sin^3 θ
Given:
sin 2θ = √3/2
Let's find sin θ:
Since sin 2θ = √3/2, we can write sin 2θ = 2sin θ cos θ as per the trigonometric identity.
So, √3/2 = 2sin θ cos θ
Since 0° ≤ θ ≤ 90°, sin θ and cos θ must be positive.
Therefore, sin θ = √3/2 and cos θ = 1/2
Substitute the values in sin 3θ formula:
sin 3θ = 3sin θ - 4sin^3 θ
= 3(√3/2) - 4(√3/2)^3
= 3√3/2 - 4(3√3)/8
= 3√3/2 - 3√3/2
= 0
Hence, sin 3θ = 0.
Therefore, the correct answer is option C) 1.
sin 2θ = √3/2
To find:
sin 3θ
Solution:
Using Trigonometric Identity:
sin 3θ = 3sin θ - 4sin^3 θ
Given:
sin 2θ = √3/2
Let's find sin θ:
Since sin 2θ = √3/2, we can write sin 2θ = 2sin θ cos θ as per the trigonometric identity.
So, √3/2 = 2sin θ cos θ
Since 0° ≤ θ ≤ 90°, sin θ and cos θ must be positive.
Therefore, sin θ = √3/2 and cos θ = 1/2
Substitute the values in sin 3θ formula:
sin 3θ = 3sin θ - 4sin^3 θ
= 3(√3/2) - 4(√3/2)^3
= 3√3/2 - 4(3√3)/8
= 3√3/2 - 3√3/2
= 0
Hence, sin 3θ = 0.
Therefore, the correct answer is option C) 1.
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Community Answer
If sin 2θ = √3/2 then the value of sin 3θ is equal t...
sin 2θ = √3/2 = sin 60°
⇒ 2θ = 60°,
θ = 30°
sin 3θ = sin 3 (30°) = 90° = sin 90° = 1
⇒ 2θ = 60°,
θ = 30°
sin 3θ = sin 3 (30°) = 90° = sin 90° = 1
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If sin 2θ = √3/2 then the value of sin 3θ is equal to: (take (0° ≤ θ ≤ 90°) (SSC CHSL 2015)a)0b)√3/2c)1d)1/2Correct answer is option 'C'. Can you explain this answer?
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