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Properties Derived from Trigonometric Identities

If sin^-1 x =...

Question

If $s i n^{- 1} x = θ + β a n d s i n^{- 1} y = θ - β, t h e n 1 + x y =$

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If $s i n^{- 1} x = θ + β a n d s i n^{- 1} y = θ - β, t h e n 1 + x y =$

(θ - α)

(θ - β)

c o s^{2} (α - β) + 2 x y s i n (α - β) = x^{2} + y^{2}

\cos (θ - α) = a a n d \sin (θ - β) = b

\cos^{2} (α - β) + 2 a b \sin (α - β) = a^{2} + b^{2}

\tan θ + \sin θ = α a n d \tan θ - \sin θ = β

α^{2} - β^{2} = 4 \sqrt{α β}

α, β (α > β)

{sin}^{- 1} x - \frac{1}{{sin}^{- 1} x} = {cos}^{- 1} x - \frac{1}{{cos}^{- 1} x} .

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