Question

Cos inverse X equal to 2 Sin inverse X then find the value off x​

Answer 1

Answer:

π/6

Step-by-step explanation:

Answer 2

The value of x =± $\dfrac{2}{\sqrt{5}}$

Step-by-step explanation:

We have,

$\cos^{-1}x =2\sin ^{-1}x$

To fnd, the vaue of x = ?

∴ $\cos^{-1}x =2\sin ^{-1}x$      

⇒ $x =\cos (2\sin ^{-1}x)$     ......(1)

Let $\sin ^{-1}x=\theta$

⇒ $\theta=\sin x=\dfrac{p}{h}$

∴$\cos x=\dfrac{\sqrt{1-x^2}}{1}$

Now, equation (1) can be written as

$x=\cos (2\cos^{-1}\sqrt{1-x^2})$

⇒ $x=2\sqrt{1-x^2}$        

Squaring both sides, we get

$x^2=4(1-x^2)$

⇒ $x^2=4-4x^2$

⇒ $x^2+4x^2=4$

⇒ $5x^2=4$

⇒ x =± $\dfrac{2}{\sqrt{5}}$

Hence, the value of x =± $\dfrac{2}{\sqrt{5}}$