Question

if Sin inverse X is equal to theta + beta and Sin inverse Y is equal to theta minus beta then oneplus x square is equal to ​

Answer 1

Given: sin ^-1 x = Ф + β and sin ^-1 y = Ф - β

To find: Value of 1 + xy?

Solution:

• Now we have given the value of sin ^-1 x = Ф + β and sin ^-1 y = Ф - β

• We can write it as:

             x = sin (Ф + β) and y = sin (Ф - β)

• Now 1 + xy = 1 + { sin (Ф + β) x sin (Ф - β) }

• Now we know that (a+b)(a-b) = a² - b².

             1 + sin²Ф - sin²β

• Now 1 - sin²β = cos²β.

              sin²Ф + cos²β

Answer:

               The value of 1 + xy is sin²Ф + cos²β.