Question

Tan(sin^-1(3/7))

Answer 1

\(sin^{-1}\left(\dfrac{3}{7}\right)=x\Rightarrow sin\left(x\right)=\dfrac{3}{7}\Rightarrow tan\left(sin^{-1}\left(\dfrac{3}{7}\right)\right)=tan\left(x\right)\)

\(\Rightarrow A=tan\left(sin^{-1}\left(\dfrac{3}{7}\right)\right)=\dfrac{sin\left(x\right)}{cos\left(x\right)}=\dfrac{sin\left(x\right)}{\pm\sqrt{1-sin^2x}}\)

\(\Rightarrow A=\dfrac{\dfrac{3}{7}}{\pm\sqrt{1-\left(\dfrac{3}{7}\right)^2}}=\pm\dfrac{3\sqrt{10}}{20}\)