What will be the value of sin10°- \(\dfrac{4}{3}\)sin310°?

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SSC CGL 2022 Tier-I Official Paper (Held On : 06 Dec 2022 Shift 1)
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  1. \(\frac{1}{{3\sqrt 3 }}\)
  2. 1/6
  3. \(\frac{1}{{2\sqrt 3 }}\)
  4. \(\frac{{\sqrt 3 }}{6}\)

Answer (Detailed Solution Below)

Option 2 : 1/6
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Detailed Solution

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Concept used:

sin3θ = 3sinθ  4 sin3θ

Calculation:

sin 10°- \(\dfrac{4}{3}\) sin10°

⇒ \(\dfrac{\text{3 Sin10 - 4Sin}^310}{3}\)

⇒ \(\dfrac{\text{Sin3(10)}}{3}\) = 

⇒ \(\dfrac{\text{Sin30}}{3}\) = \(\dfrac{1}{2}\) × \(\dfrac{1}{3}\) = \(\dfrac{1}{6}\)

sin 10°- \(\dfrac{4}{3}\)sin10°= \(\dfrac{1}{6}\)

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