Write the given expression in terms of x and y only. tan(sin^-1(x)+cos^-1(y))

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

Step-by-step explanation:

tan(sin⁻¹x + cos⁻¹y)

Use angle sum formula:

[tan(sin⁻¹x) + tan(cos⁻¹y)] / [1 − tan(sin⁻¹x) tan(cos⁻¹y)]

To evaluate these expressions, I suggest drawing right triangles.

For example, let's draw a triangle where x is the side opposite of angle θ, and the hypotenuse is 1.  Therefore:

sin θ = x/1

θ = sin⁻¹x

Using Pythagorean theorem, the adjacent side is √(1−x²).  Therefore:

tan θ = x / √(1−x²)

tan(sin⁻¹x) = x / √(1−x²)

Draw a new triangle.  This time we'll make y the adjacent side to angle θ.

cos θ = y/1

θ = cos⁻¹y

Using Pythagorean theorem, the opposite side is √(1−y²).  Therefore:

tan θ = √(1−y²) / y

tan(cos⁻¹y) = √(1−y²) / y

Substituting:

[x / √(1−x²) + √(1−y²) / y] / [1 − x / √(1−x²) × √(1−y²) / y]

Multiply top and bottom by √(1−x²).

[x + √(1−x²) √(1−y²) / y] / [√(1−x²) − x × √(1−y²) / y]

Multiply top and bottom by y.

[xy + √(1−x²) √(1−y²)] / [y √(1−x²) − x √(1−y²)]

entering that problem on the tube might get you an answer

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05