What is the sin^-1 x + sin^-1 y formula?

Solution:

Trigonometry is the branch of mathematics that deals with the relationships of angles and sides of a triangle. Inverse trigonometric functions are the inverse ratio of the basic trigonometric ratios. Let's look into a concept related to inverse trigonometric functions.

Let's derive the formula for the given expression.

Let sin^-1 x = A, hence sin A = x.

⇒ cos A = √ (1 - x²)   [cos² x + sin² x = 1]

Let sin^-1 y = B, hence sin B = y

⇒ cos B = √ (1 - y²) 

Now, we know that:

sin (A + B) = sin A.cos B + cos A.sin B

Now, substituting the values in the above equation:

sin (A + B) = x√(1 - y²) + y√(1 - x²)

⇒ A + B = sin^-1 [x√(1 - y²) + y√(1 - x²)]

⇒sin^-1 x + sin^-1 y = sin^-1 [x√(1 - y²) + y√(1 - x²)].

Hence, the formula for sin^-1 x + sin^-1 y is sin^-1 [x√(1 - y²) + y√(1 - x²)]

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What is the sin^-1 x + sin^-1 y formula?

Summary:

The formula for sin^-1 x + sin^-1 y is sin^-1 [x√ (1 - y²) + y√ (1 - x²)]