Write the value of the expression \(tan(\frac{sin^{-1}x+cos^{-1}x}{2}

1.	Write the value of the expression \(tan(\frac{sin^{-1}x+cos^{-1}x}{2})\), when x= \(\frac{\sqrt{3}}{2}\)
Answer» Given \(tan(\frac{sin^{-1}x+cos^{-1}x}{2})\) when x= \(\frac{\sqrt{3}}{2}\) ⇒ \(tan(\frac{sin^{-1}x+cos^{-1}x}{2})\)\(=tan(\frac{sin^{-1}\frac{\sqrt{3}}{2}+cos^{-1}\frac{\sqrt{3}}{2}}{2})\) We know that sin^-1x + cos^-1 x = π/2 = tan (π/4) \(\therefore tan(\frac{sin^{-1}x+cos^{-1}x}{2})\)=1

Write the value of the expression \(tan(\frac{sin^{-1}x+cos^{-1}x}{2})\), when x= \(\frac{\sqrt{3}}{2}\)

Answer»

Given \(tan(\frac{sin^{-1}x+cos^{-1}x}{2})\) when x= \(\frac{\sqrt{3}}{2}\)

⇒ \(tan(\frac{sin^{-1}x+cos^{-1}x}{2})\)\(=tan(\frac{sin^{-1}\frac{\sqrt{3}}{2}+cos^{-1}\frac{\sqrt{3}}{2}}{2})\)

We know that sin^-1x + cos^-1 x = π/2

= tan (π/4)

\(\therefore tan(\frac{sin^{-1}x+cos^{-1}x}{2})\)=1