Question

Solve the following equation

Sin^-1x + sin^-1 2x = Π/3

Answer 1

Answer:

sin−1(x)+sin−1(2x)=π3

sin−1(2x)=π3−sin−1(x)

2x=sin(π3−sin−1(x))

2x=sin(π3)cos(sin−1(x))−cos(π3)sin(sin−1(x))

2x=3√2cos(cos−11−x2−−−−−√)−12(x)

2x+x2=3√2(1−x2−−−−−√)

5x=3–√(1−x2−−−−−√)

(5x)2=(3–√(1−x2−−−−−√))2

25x2=3−3x2

28x2=3

x=±328−−√

but, only positive value of x satisfy the original equation, hence

x=328−−√