Question

x+1/x = 5/2 then principal value of sin^-1x​

Answer 1

Answer:

60°or120°

Step-by-step explanation:

x+1/x=5/2

(x^2+1)/x=5/2

2x^2+2=5x

2x^2-5x+2=0

2x^2-4x-x+2=0

2x(x-2)-1(x-2)=0

(2x-1)(x-2)=0

x=1/2 or 2

But x=2 is not possible because

Sin(θ) lies between -1 and +1

So x=1/2

θ=sin^-1(x)

sin(θ)=x

sin(θ)=1/2

θ=60° or 120°