Question

if cos inverse x minus sin inverse x=0 write down the value of x​

Answer 1

The question in its proper form is

cos⁻¹x - sin⁻¹x = 0 ; write down the value of x

Solution :

We know that, sin⁻¹x + cos⁻¹x = $\frac{\pi}{2}$

⇒ sin⁻¹x = $\frac{\pi}{2}$ - cos⁻¹x ...(1)

Now, cos⁻¹x - sin⁻¹x = 0

⇒ cos⁻¹x - ( $\frac{\pi}{2}$ - cos⁻¹x ) = 0, by (1)

⇒ cos⁻¹x - $\frac{\pi}{2}$ + cos⁻¹x = 0

⇒ 2 cos⁻¹x = $\frac{\pi}{2}$

⇒ cos⁻¹x = $\frac{\pi}{4}$

⇒ x = cos$\frac{\pi}{4}$

∴ x = $\frac{1}{\sqrt{2}}$ ,

which is the required solution.