Question

if sininversex+sininversey=2pieby3 then what is the value of cosinversex+cosinversey​

Answer 1

Answer:

π/3

Step-by-step explanation:

Given---> Sin⁻¹ x + Sin⁻¹ y = 2π / 3

To find---> Cos⁻¹ x + Cos⁻¹ y = ?

Solution---> We have a formula as follows

Sin⁻¹ p + Cos⁻¹ p = π / 2

=> Cos⁻¹ p = ( π / 2 ) - Sin⁻¹ p

So, Cos⁻¹ x = ( π / 2 ) - Sin⁻¹ x

Cos⁻¹ y = ( π / 2 ) - Sin⁻¹ y

Now, Cos⁻¹ x + Cos⁻¹ y

Putting value of Cos⁻¹ x and Cos⁻¹ y in it , we get

= ( π / 2 ) - Sin⁻¹ x + ( π / 2 ) - Sin⁻¹ y

= ( π / 2 + π / 2 ) - ( Sin⁻¹ x + Sin⁻¹ y )

Putting Sin⁻¹ x + Sin⁻¹ y = 2π / 3 in it , we get

= π - ( 2π / 3 )

Taking 3 as LCM , we get,

= ( 3 π - 2π ) / 3

= π / 3