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If sin - 1 ⁡ 1 3 + sin - 1 ⁡ 2 3 = sin - 1 ⁡ x , then the value of x is

Options

  1. A0
  2. B( 5 - 4 2 ) 9
  3. C( 5 + 4 2 ) 9
  4. Dπ 2

Correct answer

C. ( 5 + 4 2 ) 9

Step-by-step solution

Given that, sin - 1 ⁡ 1 3 + sin - 1 ⁡ 2 3 = sin 1 ⁡ x Taking sine on both sides ⇒ ⁡ 1 3 1 - 4 9 + 2 3 1 - 1 9 = ⁡ x ⇒ ⁡ 1 3 . 5 3 + 2 3 . 8 3 = ⁡ x ⇒ ⁡ 5 + 4 2 9 = ⁡ x ∴ x = 5 + 4 2 9

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