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

Question

Ryland Moore

Mathematics

5 August, 05:54

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

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Lena Alvarado · Answer 1

Sinθ = x

cos α = y

cos θ = square root of (1-x2)

sin^2θ + cos^2θ = 1

cos θ = square root of (1 - sin^2θ)

tan (sin-1 x + cos-1 y) = tan (θ + square root of (1 - sin^2θ))

tan (sin-1 x + cos-1 y) = tan (θ+α)

tan (θ+α) = t an θ + tan α / (1-tanθ tanα)