sin–1x + sin–1 2x = 3pi/2 👈👈👈👈solve

Question

We just need to apply the formula right???but how to even apply ...I am not getting the answer

 

Answer 1

sin^-1(x)+sin^-1(2x)=3π/2 (apply sin(x) to both sides and use sin(a+b)=..)

x √(1-4x²) + 2x √(1 - x²)=-1

x√(1-4x²) =-(2x√(1 - x²))+1)

x²(1-4x²)=4x²(1-x²)+4x√(1 - x²)+1

-3x²-1=4x√(1 - x²)

9x⁴+6x²+1=16x²(1-x²)

25x⁴-10x²+1=0

(5x²-1)²=0

5x²=1

x=±1/√5