Question

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Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Let y = Sin⁻¹2x , z = Sin⁻¹3x

=> 2x = Siny and 3x = Sinz.

Now given, y + z = π/3

z = π/3 - y

Sinz = Sin(π/3 - y)

3x = Sinπ/3 * Cosy - Cosπ/3 * Siny   (∵ SIn(A-B) = SinACosB - CosASinB)

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Now to calculate Cosy,

Siny = 2x/1 = Opposite side to y / Hypotenuse.

Using Pythagoras theorem,

Hypotenuse² = (Opposite side to y)² + (Adjacent side to y)²

1² = (2x)²  + (Adjacent side to y)²

=> Adjacent side =√(1 - 4x²)

=> Cosy =  Adjacent side to y / Hypotenuse = √(1 - 4x²)/1 = √(1 - 4x²)

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=> 3x = √3/2 * √(1 - 4x²)  - 1/2*(2x)

=> 3x  = √3/2 * √(1 - 4x²) - x

=> 4x =  √3/2 * √(1 - 4x²)

Now square on both sides..

=> (4x)² = 3/4 ( 1 - 4x²)

=> 16x² = 3/4 - 3x²

=> 19x² = 3/4

=> x² = 3/76

=> x = √3/76.